Dare I suggest big bend? You are in Texas. Don't know the system tho, maybe there's not much water there either.
Colorado has mostly gone bony, and all the good stuff currently running out west requires permits. You could start monitoring for cancellations in Idaho (sounds like REALLY low water there too), Westwater, San Juan, Lodore, Deso, etc.
Not sure about the non permitted stretches in ID/PNW/CA, perhaps someone from there will chime in, but that's a long trip. Not really any longer than the eastern rivers tho.
Cataract Canyon is a very easy permit to secure, but takes a week without motor assist.
Diamond down in GC may work, but really expensive tribe fees and shuttle may not make that worth it.
Wassup with the Rio Grande in NM?