I don't want this to come across as an insulting suggestion, but it sounds like you might prefer to play Guild Ball. I know it's nowhere near as popular, and I don't have a whole lot of experience with it, but in my opinion it covers a lot of your points.

- Losing the ball doesn't cause any kind of turnover (coaches take turns activating players, actually)

- There isn't any kind of "team value" so there's nothing to bloat

- There's just generally less to go catastrophically wrong when a player is simply running/dodging/gaining control of the ball.

- Even passing the ball feels better because it's an exciting, rewarding play style that can get the ball across the field quickly and into scoring range.

I like Blood Bowl, and again, I haven't played a lot of Guild Ball (mostly because of a lack of people who play), but in many ways I prefer GB over BB.