There is another thread that i came across with a lot of good information related to inverters (sorry, i do not have the link). You may want to look for it.
There are additional considerations when trying to draw a large amount of current from flooded lead acid batteries. The internal resistance causes both a voltage drop and a reduction in amp hours. I took a look at the interstate web site ( RV 6-Volt Deep-Cycle Batteries - Buy a 6-Volt Deep-Cycle RV Battery | Interstate Batteries
) and found the following:
You will see 232 Ah, with a light load of about 11.6A, over a 20 hour period . As the load increases the time you can draw that load decreases, but is is not linear. At 25A you are down to 475 minutes or 7.9 hours and at 75A it is 122 minutes. This is about 2 hours at 75A, or about 150 Ah. They do not list the reserve capacity for 150A. i will estimate it to be 1/2 or 75 Ah for the following calculations. Since you typically do not want to run your battery bank lower then 50%, this would limit you to about 37 Ah. A 1000W (output) microwave will consume 1300W - 1500W input power since it is not 100% efficient. Assuming 1400W at 120V, or 11.6A. The current needed to generate 1400W at 12 V is 116A. Assuming the inverter is 85% efficient, it would require 136A from the battery. With 37 Ah available from the battery, that would give you a run time of about 16 minutes.
Because of the internal resistance in the battery you will see both a voltage drop at the battery terminals and a reduction in Ah that can be supplied to the load. The voltage drop may be significant enough for the Alarm to sound on the inverter.
I believe the battery bank size is too small for what you are trying to do. In addition to increasing the wire size, I think you would also need to increase the size of the battery bank to (4) 6 volt batteries. Both of these enhancements would reduce the total voltage drop as seen at the inverter. Another possibility would be to switch to AGM batteries. They are considerably more expensive, but have much lower internal resistance. This means there would be a lower voltage drop in the battery and a smaller reduction in Ah under high load.
I am not an expert in this field, so I may be missing something in my analysis. When i looked at adding a microwave to my slide in truck camper, I came to the conclusion that it would not be practical to run it off of batteries.