I don't think much is needed during transport. These things fly across the country in plastic bags with no water flow. I think 3 hrs to San Antonio will be just fine. The more difficult part is making sure the ensuing nutrient spike from the move of their current tank won't nuke them and then the new tank is properly cycled enough to contain them.
If it were me, bag all sps up for transport, float them in a 5-gallon bucket, lower the water in the nano down to just above the sandbed, save all the water I removed, and make an extra 5-gallon bucket of new water. I'd pack the tank last after already packing everything else you're moving and then the tank also be the first thing you unpack when you get to your new place.
I'd then setup the old tank again, put back in the old water, and replace the corals into the tank. I'd do a water change that night or the next day depending on other moving tasks that need to get done.
Then I'd setup the new tank with the dry rock, seed it with one rock from the old tank, dump some bacterial jump start product and allow it to fully cycle... like 3-4 weeks. Then move over 1-2 test pieces and if they do well, then move the rest of your stuff.