Is this your first vape?
At the risk of repeating myself, I don't think there's anything wrong with your MFLB from what you say.
I'd also forget the Duracell idea, stick with the factory battery or one of the proven performers. The MFLB is a very very demanding device. 15 Amps, give or take. Way past the specs on AA NiMH batteries. Only a few work at all (although are top choices for less demanding duty), fewer still work well. This is why battery life is so short, power is used at an amazing rate.
Forget little solar chargers, we need way more power than happens there. The one I have would take several days to store enough for one trench. OTHO, there's a lot of very nice NiMH chargers that run on 12 VDC, getting one to work in your car should be easy to do with a common 'car cord' as the power connectors are pretty standard at 2.1X5.5mm. This is my favorite charger (although mine is a BC900, it works on 12 VDC:
http://www.amazon.com/La-Crosse-Technology-BC1000-Battery/dp/B004J6DLD4/ref=sr_1_12?ie=UTF8&qid=1408125444&sr=8-12&keywords=nimh charger
Other, cheaper, units also run on '12 Volt Wall Warts'. I'm sure you can find one. Much better than an inverter to make 120 VAC.
While it's somewhat intuitive, it also is a skill set you need to get on board with. It's only going to work the way it's designed to, not necessarily the way the owner wants. Lots of folks have 'teething problems' with MFLB, but basically none are related to defective boxes sold as new to the owner.
IMO you should experiment with different techniques, not expect to adopt some other owner's favorite one.
Good luck with it, IMO it's well worth the effort.
OF