I'd suggest you try to keep it 12V rather than using AC with the inverter.

The problem is that inverters are never 100% efficient - the best are perhaps 95%, so you're losing power right off the bat. Also, you will have an issue in the shoulder hours where the panel might be producing 100 watts but the fan is asking for 175 so the charge controller and inverter get confused. With 12V, the fan will just run at a lower power, as long as the charge controller sees sufficient battery voltage.

You can get some pretty serious 12V fans - here's a 2000 CFM universal radiator fan for $40 https://www.amazon.com/dp/B01MQFSKN3/ref=twister_B07PMRNXY7

One thing to consider is that most charge controllers are "dumb" which means that once the batter voltage drops below a threshold, it switches the load off and has to be manually reset