Could the HUP be used as an excuse for why Starfleet doesn't use the transwarp beaming regularly? I admit I know very little about that stuff, but I'm sure they could have Scotty throw in some unobtrusive exposition (a simple line or two) in the next film about how the Heisenberg Compensators lack the sophistication to transwarp beam within acceptable safety levels or something like that.
Not so sure it would make the best excuse. The Uncertainty Principle applies on a quantum level, and the Heisenberg compensators were supposed to be a <magic tech> means of working around a "position and momentum of particle A may not both be measurable without interfering with position/movement of particle A and thus rendering the measurement invalid" sort of problem. How that might be affected by transport distance I couldn't guess, but I'm thinking not very much.
Something closer to an "annular confinement beam" type of <magic tech> might be a better bet.