Interesting, I hadn’t previously been aware that taxis were picking up at the remote lot or that there was only a timeframe for both. It sounds like both rideshare and taxis will be outside of baggage claim at 9am, but things could certainly change between now and then.
There is no such thing really as “surge pricing” anymore, the fare changes all the time. That’s still rush hour so ride share will likely be expensive (easily $90-100) and traffic will probably be bad.
If you can take public transport (AirTrain to Subway or train) that may be a better option.

My international flight arrived at 4:05pm on Thursday (published arrival time so probably when the parking brake was set) and I was home on the Upper West at 5:15pm only ~$16 poorer. Google maps said the drive would have been 1h42m! Granted it’s holiday traffic now, but inbound rush hour morning won’t be a picnic either