That sounds interesting - some of it I already thought of.
But I liked the word "favour"... because you already fight in the graveyard too - to gain favour with your inner self (=zanpakutou)
To fight against enemies is one option, but maybe the TYPE should matter...you fight hollows - you gain normal favours towards shikai control... you are chaotic -> fight brutal and more vicious enemies gives you boons. you are lawful -> well, something (?), neutral is not involved.
Your alignment should matter, therefore. evilly aligned people should enable their shikai through PVP, the good ones through combat training like you described.
All increases favour, but we'd need something to drop favour, too. Depending on the type and form maybe.
After a change of form/type, you start all over, I agree. I will somewhere do a "complete zanpakutou reset" where all gets back to nothing, so people can do a new one from scratch.
"Bond Level" or "Zanpakutou Sync" ... mhm, yes, that should be a new stat --- if you're out of sync, your zanpakutou stops working, no shikai etc anymore, just a weapon (zaraki)
Also, the zanpakutou should get the same alignment you have initially.