There are many safe options for transporting and ME dog by ground…vehicles such as car, SUV, truck, van, etc.:

CRITICAL: You will have to make sure they know your dog has ME prior to even discussing scheduling. Then, you need to be thorough with your questions as to them having any experience with ME and if not then decide if you want to try to educate personally to your dogs individual protocol. Make sure you can send what would be needed including a chair if used. This one can be a challenge and a few times we have sent thru without a chair and had it sent ahead but costly. Then you would need a backup plan if your dog needs to be fed along the way pending distance. Check AND verify everything about the service you might use to make sure they are safe and will have your dogs safety as priority. Look for licensed, insured, background check if possible, company verification, etc……DO YOUR HOMEWORK because it is the dogs life you are entrusting to someone you probably don’t know!

Do your research and ask for safe suggestions if/as needed. Groups like Kindred Hearts Transport Connection (KHTC) are fantastic and safe, but not sure they will move one of these dogs due to them not having ME expertise.
Some rescues have people they know and have used safely so you can check with some in your area.
Hiring a private driver is also an option but can be very expensive.
Find ME folks along the route you need and see if they will act as “legs” in passing the dog safely from vehicle to vehicle.
Have also used a driving “leg” in-between Pilots and Paws – tricky to schedule, but can be done safely.
Check safe trucker services that can do this.
There are specific groups who only handle safe ground and use either vans or larger trucks to safely carry more dogs, but crated and secured really well.
Can ask the folks who run the rehoming megaesophagus dogs effort for suggestions since we have been involved with numerous methods of safe transport over the past 6+ years (contact thru website: https://rehomingmegaesophagusdogs.com/ or FB page: https://www.facebook.com/rehomingmegaesphagusdogs/).