Hi Pete,
So, more than a year since I bought my Upower 15kw and yours is proof they are still wiring them in that screwy way.
My 7 year old 24v/8kw pj runs my water heater in powersave mode. When on it draws about 2500w at 110v and does fine. The wh elements are rated 4500w 240v. I first tried 220v for it but the inverter would not run more than a minute at 4500w/220v. Hence running at 110v. Takes longer to heat up the tank but runs reliably like that.
The point is you get less than half of powerjack's rating as a useful limit.
For the price its still a good deal. Usually.
While still in San Diego, I used to run that 24v/8kw to run my house (240/120) on sunny days. It would do fine up to 3kw or so and a bit over for a few minutes. Yours should be fine for what you are running. You may want to add some cooling on the transformer, or just remove the bracket, plate, rubber pad and bolt from it to improve cooling. Unless you need it to be portable...