We have had a similar problem at our family rec property that is solar powered (12vdc) Had a 3000 watt ATD that would easily run our 500watt microwave visually, but took 6min to heat up a cup. We are ordering a Thor THPS-3000-12 3000 watt continious 6000W Surge Pure Sine Wave Inverter. Cost $931.99 with shipping but has a two year warranty and is manufactured by the same company that makes the Go Power brand, looks identical except in color.
Have to let you know how it works when we get it and have a chance to hook it up and try it out. We do have two commecial heavy tractor batteries coupled with 4 heavy commercial deep cycle batteries, deep cycle, not to be confused with Marine deep cycle(light duty style batteries):C