A tour could be done from the north west corner of Texas, a bit north of Texline, TX, down to Brownsville. There are roads all the way up there to the TX NM border just west of where TX, OK, and NM meet. Not all paved. I think that's a greater distance than Beaumont to El Paso, but I'm not sure. Texline has an elevation of almost 4700' and Brownsville is less (about 4700' less) so it should be a coast.

I've thought about trying that for many years but never got beyond just looking at maps.