For the G2, assuming you are set on sticking with that body coupled to the 11836, you will basically be deciding on the following rechargeable options:
2xLiFePO4 RCR123s: ~30 minutes runtime at ~full output on an 11836. (~200 lumen)Followed by some dimming, at which point the cells will be suffering from over-discharge and will require user intervention to prevent loss of cycle life.
2x Protected LiCo 3.7V RCR123s: ~45-50 minutes runtime at full output (~200 lumen) on an 11836 followed by sudden shutdown (protection circuit terminating discharge to protect the cells).
1x protected LiCo 17670: ~3-4 hours of runtime, starting at ~100 lumen, diminishing to ~50 lumen through the majority of the runtime. The low drain rate towards the end of the discharge would have the potential to mildly over-discharge even a protected cell, so user should intervene and recharge before significant dimming occurs at the far end of the useful run.
2x voltage regulated protected LiCo cells (3.7V bucked to 3V cells): this is dumb, don't bother.