Upon reading your thread, I too just browsed through the list of carrier with not so good reviews. I have pasted some other carrier reviews for you to look at. They are probably the same ones you had looked upon.
https://www.a1autotransport.com/ Top 41 Reviews and Complaints about A-1 Auto Transport
Other car carrier companies:
Best Auto Transporters & Car Shipping Companies | ConsumerAffairs
My personal opinion, I would look into Reliable Carriers. They have the orange tractor trailers. They ship vehicles for auctions like Barrett Jackson and Mecum. They do ship to independents like us. I've read fabulous reviews just now about them. Here is a synopsis of a transport in that of a Mustang:
My Review of Reliable Carriers, Inc - Auto Transport Company
Keep checking on Reliable carriers, sometimes they have a time scheduling issue. Most are happy with the service. Get everything up front on when and how long it will take to get your vehicle to you. Make sure you have the original owner of the LS take pictures of every square inch of car. That way you know if something happened or not. Then inspect vehicle very carefully when you receive it, of course you know this already.
I'll tell you a story. I bought a '96 Mustang Cobra SVT, black on black, coupe. Had 8,576 original miles on it when I bought it back in Dec. 21st '01. My Dad and I knew someone with a tractor trailer, that hooked up to a 48 ft. enclosed race car trailer. The car was in Cleveland Ohio, only 50 miles or so from Youngstown, where I live. My Dad drove the truck and trailer to get the car, he has a CDL. It was fun, the car came back perfect. Now IF you know someone who has an enclosed trailer and or truck that would be the way to go. Just making a suggestion, who knows you might be able to network with who you know to make this happen. Maybe a friend of a friend. A close family member possibly, maybe a neighbor? If you look at a poster board of peoples businesses maybe they might have a business card that offers transport services in the local library, or Small Business Development Center near a University, Grocery Store, Local Bank.
I don't know if this helped you out or not. Wish I could offer more of a solution to you. I know the things that are going through your head, the same thing was going through mine.