The Uber drop off location at Magic Kingdom is the TTC, so unless you just really want to go through a hotel and use a bus, you could just go straight there and use the monorail or ferry. At one time, you could use the hack of getting dropped off at the Contemporary, but I believe they've tightened that up and won't let you in without a dining or hotel reservation. You could run into that same issue at any hotel. We went to the Grand Floridian in our rent car on a 2021 trip to meet up with friends and head to MK and they asked for their room number or last name at the gate. The only time I've used Uber at WDW was to go to a hotel with a dining reservation or return back to our hotel, so someone else might have some better feedback.
It's been a few years since I've been to an after hours party, but my best recollection is that you can start getting wristbands at 4:00 when party guests are allowed to enter. You could always stop by City Hall on your way in to see if they'll give it to you early.