How Car Shipping Works.

Some think that car shipping is like buying airplane or bus ticket - choose date, enter credit card and done. But in reality industry works like Lyft/Uber - there is no schedule, in busy area car comes in 1 minute, in rural place it takes longer, economy level not always available etc. Making direct deal with Uber/Lyft driver is not easy - they move with no route or schedule.
Like with cab drivers you use Lyft/Uber company to match you with a driver, in car shipping there are brokers and load boards making that match. You can read what happens behind the scenes here. Even if you call local trucking company - contract will be signed under brokerage license and chances are truck delivering your car will have different company name on truck door.

Ideally car shipping works like this: you put a deposit, 1-3 days prior truck will be assigned, truck comes, you hand over the key and your car delivered.
In real life two things can go wrong:

1. Bait and Switch
2. Delays

How to avoid Bait and Switch in Car Shipping

Bait and Switch is when you get low price. Then a day prior you receive phone call asking 20% more or cancel.
Do this to avoid it:

1. When you see "100,000 reviews 5 stars" on brokers web site - click on it. Can you read reviews and write your own review?
2. When there is no way to write a review - only lucky ones get email with link to review.
3. Google "[Company name] reviews" - if you see good reviews on sites you never heard of, but 1 star reviews on yelp/BBB/google it means good reviews are by invitation only, but botched orders needed an effort to find where to write review and end up in another spot.
4. Find company address and see if they have business on google/BBB/Yelp - if it is not registered it is likely to prevent you from writing review.
5. Sharing with 1-star rated broker something like "my flight is on 5th, I really have to ship on 4th" calls for last moment extortion.

What can be done about delays

Trucks haul 9 cars, so unless customers ship exactly multiple of 9 cars daily on your lane - some cars get delayed.
Also delays can happen by previous customers, flat tires etc.
Having plan B if delay actually happens can help - you can ask friend or neighbor if they can hand over car key to truck driver if you move next day. Or ship your car 2 days before deadline.