Ask your DM.
You are combining two under-defined situations here, and there just is no good answer for either of them:
Your assertion that “therefore their base unarmed attack is considered to be neither a manufactured nor natural weapon,” is not actually supported by the rules—the rules don’t really say what unarmed strikes are, quite frankly. Sometimes they are treated as either, or both, or one or the other, or neither at all. Actually, most of the time, they’re just outright ignored.
The entire situation with gauntlets is just a complete mess.
For my money, both unarmed strikes and gauntlets are listed in the “Weapons” table, and both are listed as dealing bludgeoning damage. That should be, in my opinion, quite sufficient for mighty wallop’s “bludgeoning weapon” requirement, for either of them. But you are going to have to ask your DM if they agree with me on that.
One could easily argue that
- in the English language, “weapon” refers to an object, and
- the term is therefore equivalent to “manufactured weapon,” and that
- despite using all the rules for manufactured weapons and “manufactured weapon” not actually being a defined game-term, unarmed strikes can’t be “manufactured” per that word’s English-language definition,
- so unarmed strikes don’t qualify as weapons, and then
- a gauntlet is “otherwise considered an unarmed attack,” so everything that’s true about unarmed strikes is also true about gauntlets,
- barring explicitly those things listed there
- (and mighty wallop isn’t).