Big Bend area of Texas is an intersting bike and hike destination. Remote as you care to make it, cold nights, tepid days, no rain, lots of Texas chipseal for your riding pleasure. Big Bend State Park is perfect for mtb. I'll be returning to the area in January for a redo, partially along the ACA route that you did, but mostly south of 90.
Link to friend's report on a recent ACA tour.
Check out
Spirit Airlines for cheap flights(no financial interest.) I flew with them recently to Phx for <$200, round trip. All went well. $75 for a bicycle. They won't get you close to BB, but might work for some other destination to your liking, if there's a departure gate near you.