You sure it's a single 1/3AA NiMH that's producing 3.6v and not 3 1.2v cells wired together in a battery pack? That may have been what you meant and I just missed that, but the only single cell that produces that voltage that I've heard of is rechargeable lithium ion, and those require a different charging method than NiMH (don't know specifics). I could be wrong though.
If that really is a single 3.6v 1/3AA NiMH it might fit under the pcb (flipped like in some of the 2 batt mods). According to these comparison charts from batterystation.com it's just 1mm longer (the 1/3AAA NiMH's that tinyrc sells in the shop are a bit too short anyway) and 4mm wider in diameter. It'd be a tight squeeze, but you might could fit it in a regular bit. I thought of trying this but didn't want to carve up the insides of my bit to make it fit (slicing out plastic notch that holds old batt, moving terminals around, etc.)
I'll be curious to see what you find out.