Of all the Burny Les Paul style guitars I’ve had the custom models feel like they have a noticeably flatter radius than the standard or burst models. That would include several customs I’ve had dating from the late 70s into the mid 1990s. I had one Randy Rhodes model pass through my collection, and one of the reasons that I didn’t bond with it was the neck thickness/roundness as well as the flatter fretboard.
While I think you can trust your eyes and instruments with the data you see and observe in the catalogs, my impression and experience are that this model would tend to be flatter than other Burny models in the relative sense. The one asterisk or exception to me would be that Burny models patterned on the 57 black beauty do have more rounded profile than my other customs. I’d think that the flatter profile might well come from the fact that the RR was well patterned on Rhodes actual 1970s Les Paul Custom.
I may not be alone in this view, but I’m confident that one of the reasons that these Burny and Fernandes artist or endorser models are so accurate would have been because so many of these musicians traveled to and performed in Japan throughout the 70s and 80s, and technicians would have had first-hand access to the originals to gather specs.