Hey man, welcome to the site.
Without knowing specifics about your light it is not practical to state if/what improvements can be made.
Now regarding rechargeables, if you let them rest an hour off the charger voltage will be reduced a bit so chances are the bulb will tolerate the little extra output from the batteries.
But again not knowing any details I wouldn't want to say "awe yeah, you'll be fine.. go right ahead". Plus battery output varies as well. The idea is to find something like SureFires old LifePo4 cells as they put out about the same as a non rechargeable. So check into LifePo4 RCR123's. Amazon has "K2" brand LifePo4's.