Are these all small coins or medals?
If they are, the encapsulated coins will easily fit within four double row boxes, these boxes will easily fit within a small suitcase and this suitcase will easily fit under the seat in front of you on the plane. Just do not sit in a bulkhead seat if you wish to keep your suitcase within eye sight during the flights.
If they are not, it is difficult to carry many encapsulated 5oz, 12oz or kilo coins or medals with you on the airplane. They may be better suited for shipment by registered mail.
My experiences with TSA employees have always been positive when they are curious about the contents of my carry-on luggage.
Personally, I would not fly and I would not mail my coins. I would use this as an excuse to drive back to California and return with my coins to Texas. A roadtrip. I would enjoy seeing all of the motorhomes on the highways as people are escaping from the cities into rural America. Still, with this option, you do have to be a little careful with your one bag of precious possessions.
Best Wishes on your new adventure in the most liberal part of Texas (Round Rock?)!!!
Mark Bonke