I just called to successfully clear a waitlisted GPU for tomorrow (domestic p.s. service, new equipment), after I was checked in.
ExpertFlyer showed multiple R capacity. To second-source this, searching for a new one-way ticket on United's site showed mileage upgrades available with purchase, to anyone.
After a long hold, the agent lectured me on exactly what to say in these circumstances. Basically, as little as possible, just the unadorned facts with no inflection: I requested an instrument upgrade, it has not cleared, there is availability now, could you please clear it?
Saying that United.com is offering the upgrade with miles to new purchases is the simplest way to support one's assertion that there is R capacity.
I understand the "hang up and call again" school of thought, but some empathy for the agent's view could help the per-call success rate. There is no common language here, and the agent is attempting to match one's request against many alternative scenarios. Thus, say as little as possible, with no ambiguity that could be confused with a different request.