Harms is really your only realistic choice.
Most shippers do military and corporate business and do that fairly well. Very few do any significant amount of private business so they often have issues with paperwork.
I've shipped about 10 cars with Harms (a couple both ways.) Most were through military channels or overseas buying programs and aside from cosmetic damage I had no issues - but I always dropped it off at the port and picked it up from the port (Baltimore - Zeebrugge or Baltimore - Bremerhaven.) My two most recent shipments had issues with the CD changer ripped out during transit (Audiovox - not even decent quality) on the same car (1992 Typhoon) both ways.