I note that there is at least one pellet(/corn?) stove that not only runs on 12V but has a peltier thermopile in the exhaust that provides run power and keeps its own battery charged to provide startup power. (I think it's manual start so it just needs to run the fans until it's up to temperature.) I believe the thermopile is available as an add-on for at least some of their models.
Which doesn't help you, unless you lucked out and got one of their adaptable models, since you already have your stove. (I've heard there MAY be a thermopile designed to be hooked into essentially any stove's chimbney piping but haven't seen it...)
(Seems to me adding a thermopile to the stove and hooking it to charge your house batteries would do much the right thing: When the stove is running it would average more than enough power to make up for its load.)
= = = = =
Given that the high current is mostly for the igniter you might want to consult your manual and see if the stove can be run with the igniter disabled and manually lit. (Or if it can run with a defective igniter - in which case you could just disconnect it.) Then you could run it on a lower power alternator and reduce your idling losses.
You might also want to consider a hack like this:
- Attach a small inverter - enough to power the logic plus the fans and auger in run mode.
- Disconnect the igniter from the controller.
- Substitute a 110V relay to turn on 12V to a larger inverter to power the igniter.
- Hook the second inverter output to the igniter.
I'm presuming that the stove runs most of the time, and you're around to turn it on when necessary, so doing the same thing with yet another inverter for the motors (and perhaps hacking the power supply for the electrinics so it doesn't NEED an inverter) wouldn't make sense. Of course if it runs only occasionally, DC powering its brains and having separate inverters for the fan/auger and the igniter which only run as needed would save a lot of power.
(My own out-in-the-boonies house uses a propane stove with a miliwatt valve and mechanical stat, so it will light and convection-circulate to keep the house from freezing and the living area comfy in the event of a power failure taking out its fan and the main furnace, or a battery failure taking down the main furnace's stat.)