Dungeon World has something that seems like what you're doing here. My memory somewhat fails me, but you can basically 'act under fire' in that system, using whichever of the 6 stats work for the situation. As for the munchkins, I wish I had more constructive advice aside from 'choose a less descriptive system'.
If you need a mechanic that balances a dynamic stats, maybe a cap on moves/stats? Like, one chip per stat. Once you use that stat, you can't again for that scene/session. Or maybe when the stat gets used, you get a temporary adjustment, like a -1 forward until you rest? Maybe this is all a bit too far from the core system.