Your 522 watts at 120 volts is running current - the surge current to start the fan motor will be 3-5 times its running current, probably around 100 watts - and the surge to start the compressor, even with a soft start, will be 3-5 times running current which may be around 400 watts. The timing on those two rarely happen simultaneously so you'll need 1500 or even 2000 watts minimum inverter sizing to cope there. The raw DC current surge is most easily handled by batteries, you're not going to have 1750 watts of solar panels just waiting for the dehumidifier to start.
Money would be better spent trying to reduce - eliminate the paths ground water is taking to reach your basement - channeling roof runoff twenty, fourty feet away from the house, changing the grade of the soil to a similar radius, digging out the top soils and putting in plastic membrane to channel water to dry-sumps X number of feet from your house foundations, coating the foundation walls with water proof barrier and adding insulation, digging sump channels around the perimeter of the basement floor and adding half-pipe channels and gravel to route liquid water to a sump-pump....