Well based on your map I can already see one problem you're gonna face: The right side of your tires are gonna wear out way faster.
Made me snort

Mooshie/Schnell
Here's a map I made up of my faves out in west Texas. This is a tiny url of a google map.
tinyurl.com/n44bvcnI'm describing this from west to east
Two big ones I missed is Balmorhea State park (incredible swimming hole) and Devils River.
Starting out in Truth or Consequences (hot springs)
Head down thru Hatch valley (hatch chilies)
Over to Guadalupe Mtns. (some beautiful hikes)
Down to Valentine and the Prada store
Cross to the Davis Mtns. Fort Davis State Park and the Mcdonald Observatory.
Down to Ft. Davis , Alpine, and Marfa.
Down towards Presidio, passing thru Shafter and check out the graveyard.

Head up the river road to Chinati Hot Springs and soak a couple days.
Then down the river road thru Lajitas, Terlingua and on into Big Bend. Camp in the basin.
The River Road from Presidio to Terlingua is one of the most beautiful roads in Texas
Head out of Big Bend and up to Marathon then down to Del Rio and Seminole Canyon state park.
Then on to Camp Wood and FM 337 to Leakey One of the best motorcycle roads in Texas.
Stop in at the Lonestar Motorcycle Museum and have a burger.
On to Medina and Hwy 16 up to Kerrville, Continue north to Enchanted Rock state park.
Then either follow Hwy 16 up to Witchita Falls or head into Austin, then take Hwy 79 up to east Texas.
The thing about Texas back roads is that they are usually really good.
What reads on the map as a podunk road is usually nice 2 lane with shoulders.
I know lots of folks will have different ideas, this is just my two cents worth.
Also, I'm a big camping/hiking kinda of guy so thats what I've focused on.
Steve