Thanks for taking the time to do the test and report your finding. I'm nor my DW are coffee drinker, maybe 5 cups over 50+ years but my mother was like you so can appreciate someone needing a cup.
596 watts for 6 minutes assuming 90% inverter efficient equates to 5.8AH. (596 / 12.0 * 6 / 60 / 0.90 ). Assuming a battery can handle the 50 amp hour load (596 / 12.0 ) no reason it won't handle it for a short duration. I do think the battery holding 12V is a bit conservative with a 50A load, imagine it would be closer to 11.5V which would make a little difference but not much.
I think the biggest problem is folks don't have the inverter 12V wiring heavy enough for the length of the wire. They also don't have a good battery monitor that tells the A/HR capacity left in the battery and the A draw/charge.
