Problem solved! Sometimes it's the simple things...
I could not get the coffee maker to run long enough to test voltage and voltage drop. So I plugged in an electric heater and the inverter would run it on low for a few minutes before faulting. I found that voltage drop from the battery to the inverter was just under.4 volts. But the voltage from the batteries was dropping under 11.
My battery's were pretty old, but had performed well on all the light duty tasks like the furnace and the CPAP. But, I bit the bullet and bought 3 new group 31 fla deep cycle from Menards for $109 each. I installed them and let them charge over night. Viola! It all works. Voltage drops to 12.1 for about 30 seconds during the Keurig's most intense heating phase. Now I can have my quick, easy, no mess coffee when I travel. Thanks everyone for all the help!
