1st....lots of good advice!
I would consider a different path than the one you are currently on..
A little background on myself...
My educational background is electronics engineering, military experience primarily was in electronic communications, my current career is in industrial electrical/electronics/process automation/robotics, I have a side business dedicated to backup power, also I attend renewable energy industry expos, seminars, subscribe to industry publications, etc
Pictured below is the completely automated 8 KW (20 KW Surge) 120/240 sine wave inverter/charger setup I installed & configured in the NE La home...(my other backup setup of 20 KW {44 KW surge} Exeltech MX Inverters is in N Arkansas)
..will
automatically transfer power from a failed grid to battery powered inverter backup in a fraction of a second..
.. & it has been providing seamless backup power for my family since the late 1990's...
AC power sources for the Power Panel are an 8 KW (24 KW surge) fuel efficient, low-rpm Diesel genset..
& the Grid..
For the DC side...this 16 ea. "Golf Cart" battery configured 48 VDC DC Battery Bank (17 KWH usable at 80% DOD) shown here being replaced in early 2006 (still on this 2nd set)
Now for the advice...
..rather than trying to pound a square peg into a round hole with the gear you currently have..
(possible carbon monoxide issues with running a vehicle for extended periods with accelerated wear, possible damage to your vehicle electrical system {inverters like you describe are designed to convert DC on a short term basis from batteries to 120 VAC used for low power electronics & such, not high power devices like heaters/dryers/etc...not to invert 12 VDC from alternators...and the best batteries for this use are deep cycle...not starting batteries} ,wasting precious gasoline,
large power losses/inefficiencies in a inexpensive 12 volt inverter setup, possible damage to your new appliances with modified? sine wave inverters, attempting to sync & stack inverters likely not designed for that purpose, possible invalidation of insurance coverage with a jury rigged non-UL rated setup, possible long runs of expensive heavy gauge copper wiring needed for minimal voltage drop with a 12 volt system, lots of effort expended for little gain, possible dangerous environment for family members or non-knowledgeable others attempting to energize components in an emergency, etc )
..why not sell the gear you have ..
..& work towards a setup (like the one pictured above) that will work well for your purposes?
If you have a tractor...especially a diesel one..
..there are PTO generators that will work well for providing backup power.
Also, there are welding rigs that also work very well as a whole house generator.
Either of the above can be integrated with an battery backed inverter/charger to have an automated backup power system.