You might want to try:
out of Corpus 181 to 35 all the way up to 36 at West Columbia
take 36 down to Freeport and work your way over to 332
332 to 257 and straight in to Galveston and across the free ferry to Bolivar Peninsula and take 87 up to 124 and onward to 10 which takes you to Beaumont. From there you should be able to figure out the rest of it yourself.
If you are carrying any gas cans put them out of sight if using the Ferry.
I've pulled my 40 foot 5th wheel along that route multiple times with no issues.
I've been to all 50 States but my RV hasn't.