There are self-contained MR11 led bulbs out there, but the ones I've seen are all 12v, so you'd have to upgrade your battery too. And they're really not all that bright, probably dimmer than a 6v MR11 halogen. I think the ones I looked at were claiming 80 lumens.
Overvolting halogen bulbs by 20% (7.2v for 6v bulbs) will boost brightness by 85%.
JZ