Good report. We were in Cancun in March for family spring break vacation. Not sure if there was a problem with luggage as our daughter and her friend landed 1/2 hour before us. So as soon as we cleared customs, we met my daughter who was at the corner of happy and healthy (liquor store) with our luggage. We go next weekend to TTR, so I hope it's not an hour plus wait for our luggage.
The USA greeter is the first person who gets a tip on the trip. Slip him/her some $$ and they get you out of there fast. Finding the greeter the last couple trips has been a little difficult.
We use USA Transfers and while I do tip I don't think it speeds up you departure at the airport. It has been our experience that they get people out of there as fast as they can and in the order of check in with the greeter. The delay depends on how fast they can get the vans back. They are not allowed to wait inside the pickup area so they have to call a van that is waiting just outside. When vans are available and waiting it takes about 5 to 10 minutes. If it takes longer than that it is because they are waiting for vans to return from their last trip.