I'm sure that will have some effect, but I don't think it will be nearly as dramatic as a 95AH battery shutting down an inverter in less than ten minutes. In fact...
I did the final "bench test" of the components of the prototype system this evening. The 800 watt inverter, which I hadn't tested with the heaters before, performed fine, powering both heaters smoothly and easily for close to ten minutes. The battery, however, isn't really up to more than testing, as I suspected. It's a roughly ten year old (I get some amazing lifetimes from lead-acid batteries!) 31AH deep cycle Dell battery, IIRC. I figure it has about 10-15AH of capacity left, now, so when the inverter started to complain (while still powering the heaters) after 8 minutes, I shut it all down. The battery read 12.14 volts immediately afterwards, but recovered on its own to 12.35 volts, which translates to about 45% capacity left. There was obviously some voltage "sag" but it wasn't excessive.
Conclusion, so far: the battery/inverter/ 200 watt x 2 heater setup seems sound. Based on extrapolation only, it looks like a 30AH deep cycle battery (easier to carry) should provide half an hour's heat with this version. A 60AH marine type battery should provide about 50 minutes' worth of heat. Both estimates are based on no more than 50% (marine) and 70% (deep cycle) discharge. I still think it's worth trying a "Greensaver" battery, because of its supposed lack of sulfation when sitting partially discharged (like while the car is at work) and its (also alleged) low internal resistance, which would allow it to provide more amperage with less loss and less heat inside the battery case.
The final test is, of course, with the heater "installed" inside a car. I may try the Prius PHEV first, because of space issues and the greater interest from the PIP folks, or I may use the Leaf if my housemate objects. In either case I should know how viable this idea is within a week or so.
2013 "Brilliant Silver" SV with Premium Package and no QC, and 2009 Vectrix VX-1 with 18 Leaf cells.
The most offensive, tasteless phrase in use here is "Pulled the trigger." I no longer respond to posts that use it.