Hmmm... E6 is new idea to me. I do like it. I might have to look into it more, I think. It is firmly established in the idea of 1-5, 6-10, etc as tiers, which 5e is built around, so its actually very applicable to the game as written. I might need to adapt this for my next game as well. You'll need to cap the proficency bonus growing, of course. And I'll have to look into spells. Capping at third level spells isn't as big of a deal in 5e when fifth level spells often work as well as fireball and lightning, and some of those spells would be a shame to remove from the game. Maybe readapt things a bit?
And it could be something interesting to do with gold. 5e definitely lacks things to invest money into, so having a kind of training structure for learning things past level... Hmmm.... now I just need to adapt crafting and building rules. Anyone have any good idea for those?
Anyways, to the OP? I must say, I find your list to be rather scary. You'r egiving some classes some rather powerful benefits (cleric with their divine strike, rogue, etc), but others are being nerfed into unplayability. Like, half-caster bard. You've destroyed the lore bard in its entirety, making them all valor bards (or sword bards, if you use UA). It feels like you're creating a list of things that are "too much" for you, then you're just going to keep on building as your players switch to other things that are still effective, meaning you'll have to nerf other things to the ground... you're shutting down options, it feels like, but twisting things and making them crazy.
For instance, you took away battlemaster dice... but you've left them the ability to use things like trips and commander strikes EVERY TURN. That's pretty crazy.