>fair guess at the steady state load would be around 150 amps at 12 volts.  
>

A 75 Ah battery should then last 30 minutes, right? Although the voltage
drop would disrupt the inverter long before that.
=============
In an ideal world, in theory.  The problem is that when you load a battery at
such a high rate compared to its capacity, you won't get near the full
capacity of the battery.  My estimate of a 2C load (twice capacity) would be
that you may get 1/2 to 1/4 of the capacity, and that would suck the battery
dry (vs an acceptable discharge level).  I'd have to go do some research to be
sure, but I do know that the % of recoverable stored energy is inversely
proportional to the rate at which you draw it out.   The classic example is
WWII submarines.  They could do max submerged 17 knots for maybe an hour, or 3
knots for 18-24 hrs, same battery back.
Harvey