Is it better to use a track stop set up to dump the item as opposed to having a Give to Stockpile condition in the hauling route?
If you've got your track stops set to dump then the "Give To" option should be unnecessary. Set your stop to simply "Take From" the stockpile you want, then set desired items to everything. Since it'll only take from the one stockpile, and that one stockpile will only have items that you want, you shouldn't have any undesired stuff on the route.
On your track stops, set them to dump in a certain direction (set when they're built) and then create a 1x1 stockpile on the tile you're dumping to that includes your dumped items. Make sure you set the 1x1 pile and all your other minecart-related stockpiles to 0 bins, 0 barrels. Containers just gum up the whole works. You should be able to do this with only two stops.
At the top floor, Stop 1 is a track stop constructed to dump West. F is a "feeder" stockpile set to accept only coal. S is a 1x1 bar/block stockpile with 0 bins/barrels. You can then set S to give to your main bar stockpile or wherever you want your dumped product.
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Set the desired items to everything, set the stockpile link to take from F, and then set it to guide east when 75% full or whatever. You shouldn't need any other conditions.
At the bottom floor, it's the same in reverse. Stop 2 is a constructed stop set to dump East. F is the "feeder" pile that accepts bars, set to 0 bins/barrels. S is the 1x1 destination stockpile that accepts coal.
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Set desired items at the stop to everything, set the stockpile link to take from F, and set it to guide west when 50%/75%/whatever% full.