I haven't yet, but plan on riding more in eastern Utah - Moab area, and have one of these events on my goal list. Look for ride descriptions and maps. There's also a shop in Moab that sponsors, so presumably has some road cred (Moab is very much an off-road mecca.)

http://skinnytireevents.com/content/section/4/31/

http://skinnytireevents.com/content/blogcategory/34/64/

I've driven around Canyonlands and Moab a couple of times and the roads are much like the roads here in Colorado -- many of the interesting (hills, canyons) ones don't have shoulders. Like your experience with country roads, most drivers are courteous and give you space, although they are traveling fast. Sometimes you get the jerks....and in some of the canyons, where there can be significant traffic like Red Rock mentions, sometimes you just have to take a deep breath, stay steady along the paint, and give and take as possible because no one has a whole lot of room.