I'm not sure why you think slings became ineffective with armor. They were very effective on leather, chain and other armor, up until plate. And most weapons are ineffective against plate. Sure an arrow can pierce plate, but only after the arrow tip was redesigned. And, even then not all the time and not very deep. Swords can't pierce plate (well, maybe a critical hit), but like sling ammo, it will leave a dent. And plate armor was extremely expensive and rare. Shot placement is everything. If you have a sling and you keep fighting plate mailed fighters and you shoot for the armor, well, you are probably making other bad choices and will not live long. Aztec skirmishers would aim (and hit) the face of the Spanish.
From what I have read, the decline of the sling was not because of advances in metallurgy making the arrow SO much better, but because of the military. The militaries wanted consistent weapons and they chose military weapons not peasant weapons.
OK, there are so many errors in this that I don't know where to start.
First of all, are you playing D&D or are you recreating history?
Because if you're playing D&D then none of the above actually matters.
If you're trying to recreate history, then why are you playing D&D?
Lastly, have you heard of Schologladiatoria, skallagrim, KnightErrynt, Metatron, Lindybeige, etc.? I suggest watching a few hours of their YT videos in order to correct all the grossly incorrect information you're operating on currently.