Ah ha, thanks for the links and the info. It gave more information and added many more questions

If you manage to get the gecko going, it'd be amazing to hear what results you get.
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Any case, I just finished drafting a current state of my cooking knowledge. Formatted for more general use, so it doesn't properly reference some of the stuff y'all mentioned, but it's midnight and I ain't messin' with this much longer tonight/day, heh.
Here's what I currently pretty sure about:
There are five categories of ingredient, and as near as I can tell, so far, the actual material is relatively irrelevant beyond flavor text, so long as it's the right type. They are pure healing ingredients (fruit, meat, non-effect mushrooms, etc.), effect food (such as spicy peppers), monster bits, elixir ingredients (anything that specifies it requires cooking with monster bits), and what I've been calling inedibles, but have recently noticed some kinda' aren't (basically everything that has no heart or stamina restoration, and no effect -- mostly it's stuff like ores and ancient parts, but there's other things, too). These are the categories that seem to matter, with the particular subtype (fruit, meat, insect or whatever) not actually having an effect besides determining the name of the dish. However, there's definitely some kind of quality system involved, so while it being meat or fruit might not matter, there's definitely a difference between, say, different effect foods of the same type of effect. Haven't noticed an easy way to identify what level of quality it is... checking sell price might be the best bet outside of experimentation, but I'm not 100% sure it's not special cased in some interactions.
Healing amount seems steady and, as near as I've noticed (though I may have came across something that is another, mentioned below), has only one exception. Everything that can take to healing (which is both food and elixirs) heals at a rate of the combined total healing of the ingredients * 2. The singular exception seems to be +max food (hearty radishes, etc.), which are always a full restore, with the temp max hearts determined by the amount and type of +max ingredients added. The upshot of that, is that it would seem a single cooked +max ingredient would have the same effect as a dish cooked with four pure healing foods included... unfortunately, I haven't happened upon footage of someone checking, so I'm not 100% on that. It appears that stamina restoration may operate more or less identically, and you can probably assume with any mentions in here about healing you can substitute stamina restoring ingredients as you please.
Cooking effect food ingredients gets you, well, effect food. Cold resist, attack up, whatever. Adding pure healing ingredients adds healing as per the formula, but otherwise has no effect (I haven't seen the latter bit rigorously tested, so it's somewhat a conjecture). Adding other effect food of the same type of effect increases the duration of the effect by a magnitude I haven't seen anyone able to pin down (and may have some other stuff going on, mentioned below). I'm completely unsure what mixing ingredients does for effect strength, though I've read but not seen reports that the answer is basically nothing, and effect intensity is solely determined by something to do with (best) ingredient quality. Effect food with a innate healing amount adds its amount as per the normal formula.
You make elixirs with elixir ingredients and monster bits. Adding more of either increases duration (by an amount I have no clue about), intensity seems determined similarly to effect food. You can add pure healing food to the mix to add healing as per the normal formula to the elixir.
Mixing two different effect effect foods will produce food with no effect, and healing as per usual. +max stuff counts as it's own effect, but I've read it reported (but again, not seen tested) that stamina doesn't. Elixirs, on the other hand, seem to override all but one of the effects. What the order of priority is, and what effect that has on any other part of the elixir, if any, I don't know.
Mixing pure healing food with elixir ingredients or monster (both just makes a elixir that heals) bits will create dubious food, as will mixing effect food with either or both. Mixing inedibles with anything will generally created rock-hard food (if the inedible is wood or ore, possibly only when mixed with food or effect food; I haven't seen much done with it, yet) or failed experiments (so far as I'm aware, everything else), but there are very much exceptions here (rock salt or silent princesses being examples) and it's easily the ingredient category I've seen experimented with the least. Mixing just monster bits, just elixir components, or just inedibles fails, though I can't recall what fail state it ends up in. I've also started noticing hints that any or all of those may have exceptions.
There's particularly special parts you can knock off certain creatures that have an effect I've never seen tested but read about. You can also add a fairy to any particular combination, though I again haven't actually seen it, yet. It apparently doesn't consume the fairy itself.
The exception to basically all of that is atmospheric cooking, burning or freezing stuff with environmental effects. That throws most of it out the window, and I've never seen anyone mess with it beyond cooking apples or whatever, particularly after they found a pot. And it just now struck me that may be rather suspicious in the face of stuff like the wood/flint interaction. So there's a fair bit of potential for oddities, there.
Pretty sure there's something or another in there I forgot the exact mechanics of, but, well. I forgot, heh.
Anyway, here's what I'm unsure about:
Blood moons increase the potency of elixirs. Exactly how much, or the exact timing involved (before/after midnight, during build-up to cutscene, etc.), I dunno. No clue if there's an effect on other sorts of cooking. Knowing the exact mechanics here would be great.
There may be atmospheric effects beyond the blood moon. What exactly they are, I have no idea, and have barely noticed anyone noticing they're there or conjecturing as to their effect. I suspect these are the cause of reports of randomness from elixir and effect food creation. Currently, my biggest suspects are time of day (morning, noon, night, more?), atmospheric temperature (fairly obvious, if there's interaction, I would expect the most obvious ones to be with heat/cold resist effects, though I'm mildly terrified it varies based on individual ingredient), straight up location (cooking as close as possible to hyrule castle? On death mountain vs in the desert? Zora's domain vs other large body of water?), weather (lightning resist and thunderstorms?), and lunar phase (there's more than just the blood moon, and we know that has an effect). It's entirely possible there's more -- I'm mildly terrified of the thought that some of the fire/ice breathing/etc. monsters could cause unique reactions. Any and every attempt to experiment with these and see if there's an effect would be crazy useful to piecing together what the blazes is going on with this stuff. The more controlled, the better.
Based on an encounter in the wilderness, I pretty strongly suspect there's some very weird interactions no one seems to have yet noticed. My current big three hints is the possibility of food and ore combinations that end up as something besides rock hard food, food and ancient parts that end up something besides dubious, and strictly monster bit combinations that produce something unexpected. Immediate suspicion with that last one is to try cooking all the bits of a single monster together and seeing if anything happens.
There's definitely intensifiers in the game. Ingredients that do nothing but improve the results of the dish. Rock salt and silent princesses mentioned above are two I've personally noticed. Their exact effects I'm entirely clueless about, and they may break the standard healing formula and who knows what else. What else besides those two functions that way, I don't know. Any attempts to puzzle this out would be welcome.
I pretty strongly suspect there's going to be something I haven't seen anyone noticing going on with elemental ingredients -- topaz, elemental monster parts, etc. This suspicion is increased by the existence of the elementally aligned dragons, whose scales and horns you can knock off and use in cooking, though I don't know the exact mechanics there and so far have only seen reports they can be used to improve elixir duration.
There's apparently an odd monster bit I haven't actually seen yet, sold at a store that trades in monster parts. Monster essence. I've heard it acts particularly oddly -- turning strong healing potions into weak and vice versa. Any experimentation that can be done on that front would be great. Would definitely suspect it's a possible key to pure monster bit recipes.
... there is blue fire in the game. Does it change things? Can you cook with it? If not pot, what about atmospheric? If there's a suspect for what could enable valid food+ancient part combinations, that would be it. And... are there other fires? Haven't personally seen any, but...
E: Though bloody hell, it just really hit me how blatant a hint one of those failed cooking recipes might be.
"Ultimate survival dish"? Made of monster parts? If that's not a veiled reference to some sort of necromancy, I'm not sure what is. Could be a red herring or me reading too much into it, of course, but...
E2: good gods, now I'm wondering if burning a stalfos skull in a pot's fire before cooking would do something
i'm going to sleep now
can
can you put those little rock monsters in a pot? you can pick them up. maybe you can cook them. and if you can... cucco directly into the cooking pot?