I had similar issues and was considering adding a diode and another battery...bear with me as the size of the cables is not the problem. Check the voltage at your batteries compare to the reading on your inverter while running the microwave...takes 2 people. I had a little over 1.1V difference so cleaned and tighten all the connections I could find including those in the back run box....just tighten them. On your negative house battery cable you have the shunt that measure your amps and cleaning them did the most good. I now have 0.4V difference which was my goal and as a side benefit my 10K will start without using the boost or cranking the engine.