There's nothing stopping you from using 'down' for both attacks like stomp and for dropping through ledges. Basically if you hold 'down' then press 'kick' you stomp, but if you instead press 'jump' and only if you are on a thin platform you drop down.
As for auto ledge grabbing, while that can be a problem you could always consider special 'ledge attacks' where the character quickly pulls themselves up into a rolling kick or some other attack. Or, if you hold 'down' whilst on the ledge then press 'attack' you could do a dive attack off the ledge. i.e. turn the weakness of automated ledge grabbing into a new tool for combos and moves. Fuel for thought.
As I said definitely look up guacamelee, that game does a lot of what you're trying to do and there's no shame in looking up what someone before you has done and taking what works.
I'd also look into how they handle movement and ledges in Super Smash Bros as while that's a pure fighting game, it balances solid combat with snappy yet simple platforming controls.
But of course that's not to say it wouldn't take a lot of work and thought in overhauling your control scheme. Rome wasn't built in a day. And you don't need to take in everything I've said. Pick and choose what suites your project best, I'm by no means an expert myself.
And finally here's a little rule that's always handy to keep in mind, "Keep it simple stupid".