Aaaah - I finally got on your thread!
We sent our daughter's car from SJ to NC last year. We searched eopinions for references & finally decided on a company. Its expensive - about $1500 - but, she didn't have the option of driving the car out there.
The thing to remember....the car goes lots and lots of places. Her's was picked up about 2 miles from us (door - to - door is more expensive) & was dropped off at a lot. Between CA & NC...it went to AZ, then to WA, then to IL, then to NY then to NC (where it was dropped off) & the truck finally dropped its last car in FL or somewhere down there.
PM me if you want more details. You need to allow time...time..time! The car left here June 30 & was dropped off July 17, I think. They stored it until she was able to get it. You can't send it with much gas in it & they don't insure it for contents, so you have to leave it empty, for the most part.
In our experience, it wasn't driven (except for the few tenths of a mile or two to put it on and off a truck & drive it into & out of a storage lot. There was no apparent trash on the inside & it was washed when she picked it up. No damage to the exterior.
Let me know if you want more info.