I see Punk doing very well in the Rumble lasting the longest and in the final 5 or so. The only thing I can think of to really get this feud started is to have HHH come out and screw over Punk and get him thrown out of the rumble, starting the feud for WM XXX.
Either HHH or his lackeys will eliminate Punk. Best case scenario would be Punk and Bryan as the final two in the rumble, and the two of them go at it for a long while before Bryan winning.
I can see Kane entering the Rumble on behalf of the Authority, dominating for a while and Punk eliminating him, leading to HHH coming out and distracting Punk so Reigns (or any member of the Shield) can eliminate him