I guess there can be differences of opinions as to what "administratively feasible" means. I think if the VCP filing could result in a DECREASE of the participant's account balance, there may an issue of "protecting plan assets" and the known difficulty of trying to get overpayments returned. But if the VCP filing could only INCREASE the participant's balance, then what is the impediment to a secondary distribution? An initial distribution of a known balance is easy. A secondary distribution of a corrective contributions is likewise "easy." Last I checked, the "cost" of doing a secondary distribution is irrelevant in the decision. If it was the plan sponsor's error, it is the plan sponsor's burden to make it right.
The "best" approach (IMHO) is to follow normal plan procedures and precedence in processing the distribution, and if necessary, make a secondary distribution AFTER the VCP correction has been made - especially if that determination may be months, if not many months into the future.