Funny I didn't think of this when I made the initial post. I was trying to think of the last time a mainstay player from a championship team signed with a division rival, and nothing was coming to mind. After all, it doesn't happen very often—imagine if Kevin McHale had signed with the Sixers, or if Kobe Bryant signed with the Clippers (which almost happened, but that's besides the point).
Then it hit me, the most obvious comparison of all: Dennis Rodman, who I even mentioned. Lockdown defender and voracious rebounder on Pistons championship teams, he (eventually) signs with the Bulls and accumulates a few more rings. It obviously would have been a lot more similar had he gone to the Bulls in '91, when the wounds were still fresh (and he was less crazy), but I couldn't come up with anything closer. Anyone?