You correct Richard.. they are great. I have a pair of them with the connectivity kit. I did a lot of research, probably too much, to find the best price.. tightwad that I am.. squeek squeek.
The best price I found was at Speedway Sales which included shipping (and no tax).
Click HereI do believe you can do a 6 hour cook quite easily on any battery that is capable of providing 70A assuming a 90% efficiency rating of your inverter. Certainly a deep cycle battery like those used in boats, RV's, etc would be inexpensive and QUIET.
A little more info on the battery option. First, I don't know what the cycle times are on the heater.. but, just for some assumptions, let's say it takes about 20 minutes to get the box to temperature (it'll likely be more time) That's (at the battery) 70A for 20 mins. Then 7A for say 6 hours. Or 21AH to get hot then 42 AH to keep it hot. So the sort of battery you would be looking at would be around 60AH. You need to make sure though that it is a "recreational" type meant for driving inverters and stuff and not meant as a car battery. Or it won't last long. So, even if the times above are not correct, a 200+AH deep cycle battery would more than do a 6 hr cook.