I stood firm on "measured height" for years, but eventually caved & have "seen the light". We now run stamped height & maintain a list of the oddball tires that are considered legal - for example, MRA class 2 is a 37" stamped height limit. R85 Buckshots are considered a "37x13", so those are legal. A 38.5X11 that measures 37" would not be allowed in the 37" class.
On a side note, Interco used to make TSL's in a 13X37 size & sometime around 1985, they changed the stamp on that tire to 38X12.50 - exact same tire, same mold, verified by Interco. And ONCE in awhile, a set of those old 37's still show up. It's for that reason, I've always preferred to make the 37" stamped height class 38.0". BUT, too many guys assume that they can run 38.
5's - or worse, argue that their 38.5's are in fact 38.0's. They all get that same deer in the headlights look when you wipe the dirt off & show them the sidewall stamp, though

Anyway, those old 37's will be gone one day, so 37 is probably a good limit.
Oh, and the question you didn't ask but wondered, yes MRA classes limit tire diameter based on the sidewall stamp.
Scott