So after reading this thread I decided to play for nothing but battlefield. I got up to level 5 or 6 I think--took 110 hits to finish. After that I think I discovered a game bug, because the dmd was saying I needed 188 hits to open the battlefield.

Decided to play the game out (I did accumulate like 5 extra balls in the process), ended up with a GC score around 2.5 billion! Was 2 shots from finishing final battle too--that would have been huge.

After the success of my first attempt at a battlefield strategy, I tried it again. This time, I put up 2.7B and completed final battle! Note that my previous high scores were around 1.5B. So the battlefield strategy is definitely useful for big points. Complete battlefield, collect extra ball/start mode, rinse and repeat. Definitely not wise to do in a tournament with no E.B., but fun at home!