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. If it does not show you independent web site like Yelp or Google with reviews - this is red flag.
2. Google "[Company name] reviews" - thousands reviews with 1.5 stars average is bad sign. Read couple of reviews.
3. 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.