This certainly not a recommendation, but one service is
uShip. Like most others, this is really just a dispatching service; the actual transportation is done by someone arranging work through them.
I used a dispatching service (local here, not uShip) twice to move the same trailer, getting different truckers for the two trips, with similar pricing but different levels of service. If you can get a recommendation for a specific operator that someone has found to be good - not just the dispatching service - that would be ideal. My trailer was towed on it's own wheels, but it was large and tall - putting it on a flatbed would have been very expensive. ETI has Escapes shipped on a trailer or flatbed truck.
If you like unscripted ("reality") shows you might find
Shipping Wars amusing... but you might not want to watch it before entrusting your trailer to one of these people. In this show the dispatching service was uShip, but I don't think that uShip really works the way they show, just as most businesses in "reality" shows don't really work the way the shows suggest.