I cycled most of the ST last year, albeit in the opposite direction to your planned ride.
I was mainly staying in motels and had little problem in finding accommodations, with only a couple of exceptions. From your post, I don't know what your preference is with regards to motels or camping.
I personally, would recommend sticking with the ACA route out of Van Horn through to Fort Davis. It is a challenging ride, especially riding W to E, and there are no services available at Kent, however the country side is spectacular.
There is a cyclist's only hostel at Marathon, and information is available at the pizza place on the main street. There isn't much available between Sanderson and Comstock. I couldn't find any store open in Dryden when I passed through. You will need to time your arrival at Langtry if you are relying on stocking up with provisions. The only store is on US90 which wiil be on your right hand side, before you head down into Langtry. There is nothing in the town iteslf, other than the Judge Roy Bean museum. It has clean rest rooms and wi-fi. You can pitch a tent alongside the community centre hall, but there are no amenities, other than a water hose. There is a donation box where you can drop in a couple of dollars. There is also a trailer where cyclists can stay, but I never saw the owner, and I am not really sure of the protocol.
Comstock is very small but does have a motel. I didn't stay in Comstock.
Road 334 out of Bracketville (ACA maps Section 4, maps 52 & 53) has a rough surface, but the surface improves once you turn onto Road 55. There are no services between Bracketvill and Camp Wood, so you will have the best part of 50 miles without services. The hills around Leakey and Vanderpool are challenging.
Out of Bastrop, the ACA maps take you through Bastrop State Park(ACA maps Section 4 map 61), but these roads were closed when I came through last year, so maybe you might want to check with them beforehand. No big deal and I rode state 71 for this section.
There is no shoulder on State Rd 150 between New Waverly and Coldspring (ACA maps Section 5 map 67) and there was lots of traffic when I rode that section. It was early morning out of Coldspring so it might have been early morning commuters.
There is no shoulder on Country Rd 363 between Kirbyville and Bon Weir (ACA maps Section 5 map 71) and this road is used by trucks.
If you have ridden SF to SLC solo, this section of the ST shouldn't cause you any concerns.
It really is a lovely ride and I hope you enjoy it.