To encourage the use of other battle types, why not offer a different type of reward for each one?  Drop rates don't have to be every game, maybe just 1 in 10 or even less.  A few ideas might include random drops like these:

 

WaW:  Already has xp boosts, no need for anything else

Skirmish:  Random XP boost (maybe 30%)

GB:  No need to boost anything here

GBII:  HH drops

Select Mode:  CV Select-Experts / BB Select-Vets / SS Select-boosts / all others-HH

Blitz: Experts

Night Battle:  Smoke

Op Convoy (if it's ever fixed):  Mines

 

 

Or just offer all items at random drop rates in every room except GB and WaW.  This way no matter what type opens up, it will likely be filled.  

 

I know this means $DE releasing their wallets a little bit, but it would add flavor to the game and probably bring in more players along with keeping those who might otherwise get bored of the game and leave.

 

Thoughts on this?