I have found that on a Sunday night, it is near impossible to get a large vehicle tow. The shops have a small wrecker on call 24-7 for emergengies, but the drivers of their larger trucks are off the clock. Whether it's the shop that says "nothing available" because they are too cheap to pay the driver overtime or the driver says "not available" because he doesn't want to waste his Sunday night is anyone's guess.
If AAA can't get you a tow, THEY will call the Highway Patrol to get you off the road. The Highway Patrol has non-contract tow trucks they can call to get you off the side of the freeway. It may just be to a parking lot, but it will be off the road. Then AAA will get you the tow the next morning as part of the same service call.
Good Sam fails in that if they can't get you the tow that night, they just leave you to deal. They won't call the highway patrol for you to make sure you are out of danger and off the road.