If that kind of money is not important then I would go for the Xantrex...they are one of the top names in inverters in at least the marine field, Tarce being another.
I just wrote somewhere about the power required for my FE100...might have been on my web site. Briefly as possible (for me) a deep cycle battery usable current is good for about 1/3 of its rated total amp hours. Therefore., if you had an 80 AH deep cycle battery and you were going to use that on the FE100, or similar internal works, you would use about 1.3 AH for the 4 minutes at startup then about 2 AH each hour therafter. Hence, that battery would give you about 22 hours of usage...IF...you never turned the unit off to cause it to go into the start mode again. A cheap inverter might not have a good enough modified sine wave, a true sine wave is what the FE100 controller really likes. Three hundred watts will be enough. The efficiency is about 85%, you mudt caluculate that off of the 22 hours I stated above.
Looks like you can run the FE100 controller down to about 11.7 volts dc then the LED's start flashing and everything stops!
Watch out for a problem of gasses from the battery being ignited or getting into your food. If you go gel cell you don't have these problems and the battery can be used on any side and even unside down, however when upside down you loose some of its total capacity. But you do need a charger that is specficily designed for charging a gel cell or even an AGM! You could wire that type of charger to your vehicles charging system for those batteries. You should have a deep cycle charge mode for the wet cell deep cycle battery for longevity but it isn't necessary.
You can buy special caps that retain over 90 percent of the water in the battery...they seldom need attention...each cap is about $10 (times 6 cells = another $60). These are great if you build your batteries into a place that is difficult to access, like in my last sail boat!
When you purchase a battery look at its born date, wet cell batteries begin dying as soon as they are filled with sulfuric acid.
I spoke to Ortech Ind., the previous manufacture of the orginal controller for the FE100 and Traeger. I asked if it were possible to change the firmware and hardware to be able to turn the start mode on or off or a bypass should there be a power glitch. They no longer are involved except to repair the older controllers. They do it for a flat $60 including shipping back to you. They said it would be possible but would take a rewrite of the firmware! They won't part with the program, I asked! I think we ought to all write to CS and get them to do this but they wil probably have to go to Traeger! Back to square one!
We could easily install a switch, I think in the purple wire...I might be wrong, don't have the wiring diagram in front of me. But that will not stop the auger feeding pellets for 4 minutes no matter what the temp is...hence, heat peak! I have sat there for those many minutes opening and closing the door to bleed out the heat! But at least the single battery would hold up not firing the bypassed hot rod.
P.S. Consider the cost to have that heavy puppy shipped...go buy a deep cycle battery and 300 watt inverter at your local marine store or Wal Mart! Golf cart (Exide GC5) batteries at Wal Mart used to be $47...you'll need 2 (they're 6 VDC each)and you'll then have 200-225 AH and a
LOT of
VERY DEEP cycles!!! ...Exide GC6 is better, Optima is one of the "Rolls Royce" but Wal Mat doesn't carry these.
Told you this would be brief!