The things I try in various cars when CarPlay acts up, besides all the things you've already tried and done:
- 1. Hard reset your phone (NOT a Restore -- just a hard reset, info here
2. Ensure your iPhone is up to to date/run iOS version updates
3. Understand it's not possible while on a road trip, but turning off the car/leaving it completely off ("Don't even look at it") for at least 30 minutes
4. Now more drastic things -- Reset All Network Settings (you'll lose your wi-fi passwords and such, may have to reconnect other Bluetooth devices)
5. The dreaded Restore your iPhone (from an earlier iCloud backup or a backup done on your Mac/iTunes on a PC)
#'s 4 and 5 are always a last resort as they're a bit destructive and time consuming. All of these are, of course, when you come to the conclusion that your iPhone is the problem and not the car/car software (which of course I'm sure you've checked to ensure it is up to date). Finding another vehicle to try your phone with its CarPlay unit is something I always try when possible, at least before trying #'a 4 and 5 -- and after testing for awhile in another vehicle, you can decide which of the two (the iPhone or your car) is the problem.