I've had experience rebooking due to IRROPS both at the airport and on the phone. I agree handling at the airport is 1000 times easier. The only problem is you have to wait and if there are only a few seats left on your desired rebooking then you may be SOL.
My experience is that the phone agents can't see all partner flights (likely SHARES). For instance there were ~6 or 7 available flts on PHL-BDL, but my agent only saw 2. I had to have my corporate travel agency call them to tell them there was availability and then the UA agent had to receive approval from a supervisor. Essentially it was a waste of a few hours.