Washers and dryers are now considered baby loads, even combined with a few fridges, computers and an Air con running
IMHO it will come down to the physical size constraints you have, the weight (toriod) and the available battery space, the main Inverter limitation will likely be keeping the Toriod cool when compromising size and weight. A smaller toriod limits your run time with continuous loads above a kW or so, if the secondary winding is up to it then forced cooling of the Toriod would allow you some decent run time for a tiny-house.
For a small installation, the limitation will likely be the amount of solar you have available, all the batteries in the world are useless if you can't charge them. IMHO Solar rules and the rest follow. In a tiny-house there will obviously be compromises, I'm assuming that you may need to plan for no available AC power ? If not, the battery verses available solar equation could vary.