Getting an inverter that's big enough to start the sewage grinder/pump will be costly.
It's not necessarily the amp draw when running the pump--it's the starting surge for it.
Might be possible of course, but it won't be cheap.
Solar + batteries to have a few weeks of backup is pricey too.
Might think of using a smaller (3-5kw) gas/diesel generator for just weekly or bi-weekly pumping. It would be good for a backup system for the house too.
Probably be cheaper in the long run to just run buried UF cable and the grid power from the new house, though.