See, I just think power should make fights easier, but not be the method by which you can win them. Those 200% attacks that are "so overpowered" due to your stats could simply be mitigated by the downside of those attacks... Or it requires precise use of the skill in combat in order to do any damage at all.
You're just having a little bit of trouble thinking of ways to tinker with combat in your game without relying on the stats (the extra ATK and DEF mentions are where I'm getting this impression).
Let me just present to you a scenario that does exist in my game, but it isn't in the "demo" portion of it. It's meant to teach players the value of "Stun", which leaves anyone inflicted absolutely immobile until damage is dealt to them. I have two healing mages that have full 100% heal abilities. They cast it, whomever it hits gets 100% of their health back. It's a full heal. The last creature is a powerhouse that does really powerful attacks to players. Having a lot of stats would help you kill these enemies with ease, sure, but if you don't kill one... it gets a heal, and you're back to square one. So, the player is only given a single character at this point that can even inflict "Stun" at all, so they have to choose what they're doing with it. There are lots of options at this point in who and how you can win the fight. Do you stun the healers and use your defense to kill the big guy who does a lot of damage to you, therefore, eliminating the threat? Or, do you stun everyone except one of the healing wizards so you can focus attack them and take them out one at a time? The stats, themselves, don't matter a whole lot here, because it isn't about how much damage you can do, it's about using what skills I've given you intelligently. The healing wizards can't use their skill on themselves, but they can use it on anyone else. Higher stats at that point just means less hits to kill them and maybe you can take more attacks from big burley guy. It isn't really how you win, it just makes winning easier. If done right, a player could even potentially keep a single monster stunned all fight while inflicting damage on it.
It's okay to have your stats matter insofar that they make combat easier. It isn't okay to have all of combat revolve around those stats. If your combat uses the stats as something secondary, then you don't have to worry too much about trying to balance things out. A few levels here or there shouldn't totally matter in combat. If they do, your combat isn't varied or interesting enough. I mean, yeah, everyone has the power fantasy of wanting to do as much damage as humanly possible and being nigh-indestructible... But, it's okay to temper that with making players have to think about it. In my combat scenario, stats for that fight only mattered in-so-far that it didn't affect difficulty until stats ran somewhere above and below 20 in either direction (for reference, I use low stats, and at that stage in the game, most quests give 1 or 2 points in any particular stat upon completion... so 20 point differences is fairly large in my game).
Just think about wrenches you can throw into battle. Ever play Final Fantasy 6? That first boss, the snail thing? Easily murdered, yeah, but if you attack its shell... it insta-kills whomever hit it. And, it spends turns inside its shell every few turns, so you had to spend time defending or healing up while waiting for it to come back out. Stats would speed this along, yes, but not allow you to win it... Learning the attack pattern lets you win it.
Honestly, that's all stats should ever do. Speed you along. They shouldn't be the reason you win, they should be the reason you win FASTER. Or, they should be the reason you don't need so many healing potions.