GMforPowergamers
Legend
could work as a modified escalation die from 13th age.I don't like such recharge mechanisms to be honest. I thought more along the line of: you get +1 to every d20 roll for each encounter after the last long rest or you get a pool of d4's that you can add to a single d20 roll per encounter. This pool starts at 0, recharges every encounter and you get one exra roll after each encounter.
I like anysystem that says "if you push on a bit we will help you push on a bit not punish you for it."