They do make commercial/industrial inverters that will handle the load and will provide reliable service. As you might expect, they won't be inexpensive. As expensive as they might be that still might be economical relative to other options.
Have you done the math to see how long you can actually run your power system? I can imagine fork truck batteries that are no larger than auto batteries - but have seen plenty that are as large as an auto (almost!!).
90 watts x 7 days x 24 hrs/day is 15,120 watt-hours. 220 vac x 30 amps is 6,600 watts - or a little more than 2 hrs run time. The solar panel won't put out 90 watts continuously so you aren't going to get much run time unless you have a supplemental charging system. The math isn't precise but it gets you thinking about the order of magnitude.
There are absorption type refrigeration systems that are used in RV refrigerators. They use heat and an ammonia cycle - the heat coming from resistive element. It's not particularly efficient but it works. If you could provide the bulk of cooling that way then a common, low cost invertor could run the evaporator fan and other appliances. I'd like to think that someone makes a residential version.
Sorry it's not a schematic but I hope to have been of some help. Good luck.