The most energy and space efficient source of 6 V DC for a trail camera
I have actually first come across similar cameras about a month ago, possibly the same model or manufacturer.
A customer was confused as to why they worked on batteries but not on an adapter. He thought some electronics failed on the board. I discovered that the camera actually needed a specific voltage range or it wouldn't even turn on. I don't remember exactly, I think it was from 4.5V to below 9V. He actually had a power supply whose voltage was outside of this range (I think 12V).  

Anyway, first to correct you: connecting 2 cells in parallel can be dangerous only if their charge levels vary greatly (like more than 0.2-0.3V I think), so all you need to do is make sure their voltages are within 0.1-0.2V of each other when connecting them together and they will just work great afterwards.
If you are using a DC-DC converter, make sure that it has a VERY low quiescent current (the amount of current it uses with no load whatsoever, for running its own circuitry).  

Before trying anything else, I would suggest you measure a camera's current consumption at 5, 6, 7 and 8V and see if it varies significantly (especially with the IR LEDs turned on).
Your solution might be as simple as 2 Li-Ion cells in series, without any conversion. You would just have to make sure they disconnect before the voltage of either cell drops too low (below 3.2V; depends on its chemistry). If the cells have circuitry on them, that's good, but you may want to have your own adjustable, micro-power monitoring circuit.  

One tip: lithium cells can be recharged many more times if you use only 50% of their capacity (from 30%-80% charge level), so you could employ that tactic.
Another tip: You could include a ~7.2V mini solar panel to charge your batteries. It wouldn't be much larger than the camera.