I’m not sure post #3 is totally right.
Most wheelchair passengers are brought into the TBIT Customs hall, and often have to wait for another pusher. That’s what happened to me a couple of weeks ago. The delay was enough for me to miss my connecting flight. I had a 2 hour connection, and my inbound flight was a bit late. 3.5 hours is a good idea for a connecting flight. Hopefully this was all booked under one itinerary.
You are able to recheck most bags once you exit the Customs inspection area. You might check with AS. I know DL, UA, AA and others certainly can. Dragging the bags with you to another terminal to recheck is no fun.
In my last few visits to LAX, they have a handicapped shuttlebus pick you up. If you are able to walk up the bus stairs, and take a normal seat, great. Otherwise they have a lift for a wheelchair. Then, at your correct terminal, a wheelchair pusher meets the bus, and takes you inside the terminal to another holding area. Another person comes later to take you through TSA security and to your gate.
They usually leave you at the gate, and then return for boarding. I have 3-4 pushers on an average inbound Intl trip. I would recommend bringing some US currency for tips. I usually have a pocketful of singles and fives.