First, Dr. X cannot stop the transition by not giving up his position, which I presume is through a brokerage account feature. The trustees have authority over the assets, and they presumably take their direction from the investment fiduciaries. Second, I agree with Austin, his account should transfer easily. I'm not saying you should say who it is, but I'm really curious who RK A. Service agreements seldom get into detail about how the termination of the contract will work, so I'm guessing this function was not addressed in your service contract; however, i would take a look and try to confirm that.
At this point, the investment plan fiduciary is in a serious bind. There presumably has been a decision that participants will be better off if you transfer to RK B; however, this move isn't occurring. It can be sort of a cheat on this message board to recommend that legal advice be sought; however, in this instance I think you don't have a choice. You need a legal opinion regarding what to do. Do you prevent the other participants from getting the value of the move or do you prevent this one participant from getting the value of staying until the investment fund liquidates? Get the opinion, then follow it.