If you are in the US, Mexico and Canada, but you will need to contact your carrier to find out what restrictions you might have with your insurance in those two countries, otherwise here in the states all you need is your current health insurance, it will pay for everything minus your deductible, and co-pay.
What you do need to find out is whether or not your current insurance covers hiking and biking in excluded areas of the US, or will they cover you if you are at altitudes greater than 2,000m. Find out if your insurance will cover emergency evac in remote places.
I agree with another poster that said it very simply, if you don't need additional insurance now, you're not going to need it on the Trans Am.
Keep in mind, if you buy any other coverages you cannot collect twice, both insurance companies will find out you have two policies, and they'll decide who will pay, while the other may not have to pay out a dime!
It is best not to listen to me or anyone else about your questions, you need to contact your health provider and get a detailed explanation as to what to expect and if there is any extra coverage they can recommend.
What will, or could be more important than insurance if you're worried about a catastrophic injury is having satellite backup emergency communication radio in case you can't get cell service and you need to call for help, and hopefully, someone can get to you fast before you die from injury, thirst, or exposure. Even if you're going with a group, someone should have a sat radio, but ask to find out, if not get one, because even if you're in a group they're not going to be able to get you out or send someone up ahead fast enough to maybe save your life.
I will add this, if you're not racing the TransAm, then the chance of a catastrophic injury is pretty slim.