I suspect that turning Slog into some other slime will be difficult. Let's look at the one time we have: We needed to use a semi-rare consumable (a Fire Shroom from a specific arena fight, which wasn't gained automatically and needed time taken out of the fight to get IIRC) to temporarily turn Slog into a (powerful) type of slime. Assuming for the sake of argument that the power of the slime and the temporaryness of the transformation balance each other out, turning Slog into some other kind of slime permanently would probably require a somewhat rare and/or hard-to-get item as well.
Actually...I think it was a Mega-Shroom. As in, those ones that turn Mario into a massive stomping maniac? Those only give the ability for a certain amount of time. So there's a chance a sword could be permanent.
On the other hand, as a sword is much more common than the Mega-Shroom and permanent is obviously much more desirable than temporary, the resultant permanent buff would be MUCH less desireable than the King Slime one.
Also remember that the Shroom was a consumeable and swords are...not.
And besides, I'm sure FFS would pretty much let us do anything as long as it doesn't affect the plot TOO severely.
As long as we work at it--Freeform's not that Monty Haul.