Not to encourage you to run 191 south of Alpine because there is a tunnel clearance problem in the Morenci area, but we've been doing it for many years with a 34 foot Class A - - though we are only 11 foot 4 inch high.
There is a 400 foot long tunnel with a marked clearance of 12-7. It has a curved "roof" so that clearance would be on the outer side of the lanes.
And a short underpass in the area marked 15-0.
Down in that same area there is also a 40 foot truck restriction - which could be overcome by driving a tow vehicle through that short area if a person were so inclined.
As I guess one could assume I don't think all the dire warnings about that stretch of road are justified. It's a long lonely road with basically no traffic and great views.