I tried something similar when trying to power some trail cams with other than alkaline batteries. I bought some small motorcycle like batteries off ebay that said AGM and they died quickly. The charger that came with them although rated correctly seemed to blow out one cam so I threw all that stuff in the trash and went back to duracell alkaline after also trying the Amazon alkaline AA batteries. Amazon AA are not comparable to Duracell. They are cheaper so given their performance they may be cost effective for some.
I will also look forward to others ideas. Thanks for posting.