The big test is now to run the microwave and see how much voltage drop you get. On the monitor, set it to read voltage and see what it is, then turn on the MW and note the lower voltage. Say it drops 0.8 volts (could be more, whatever) Now it will slowly drop from there as the MW runs for a few minutes.
This tells you how low the batts can get before you can't run the MW, or the toaster for breakfast. If it drops 0.8 and gets down another 0.2 and the inverter quits at 11 volts, then as long as voltage is above 12.0 you can do it. (but recharge the batts later that morning!)