Hi SoundGuy,
I would stay away from group 31 jars.
Move to a Group 29 AGM. The lower resistance design will power the toaster with easy if the cables to the inverter are short and fat enough. I have found the AGM charge considerably faster, too.
When the 12 volt Marine flooded were on their last legs, I would start the engine on my class C to support running the microwave. The micro would still run without the alternator support, but the inverter would scream at me.
My "new to me" batteries are telecom tower AGM take outs at 139.2 amp-hours each. They are unusual as they are a surplus acid design. That means I have to be careful about depth of discharge. I basically treat them as if they were flooded--except for charging and float voltages.
They weigh 105 lbs each and are a fairly tall battery. They may be available at your local interstate store and the cost was $124.00 each, with no core charge.