The solution I followed involved the Driveline library. The rope drum object in that library has its source code available, from which it was easy to create a custom version with the drum radius as an input signal.Then the translational multibody interface (rather, my own version of that block since I'm using 2020b) connected me back into the multibody visualization world.
I still have a strange issue here where I can't use the measured angle of the drum as part of this radius input signal without putting a unit delay on the angle feedback. It raises an error that the initial radius of the drum cannot be zero, even though it is not. I believe this is some kind of issue with the mechanical sensor elements holding everything downstream of their sensor lines low at the simulation build time, but I have not investigated that in depth.