I don't understand the issue. You book your ticket, you upgrade it to C using KF miles. Then the flight is now in Biz but the underlying Eco fare can still be credited to LH M&M. Just give them the M&M card at check-in, make sure they remove the KF number (sometimes I insist that the BP does not show SQ# at all and only LH status) and the mileage should go to the LH account. Works fine.

Vice versa, in the past, I had an SQ flight (FRA-SIN on 744) upgraded from Y to C using LH eVoucher via *A upgrade facility) and then credited the miles (for the Y ticket) to BD later on. Worked without issues. Just becasue your KF FFP number may get added to the reservation due to the online upgrade doesn't mean it can't be removed later on.

Similarily, I have made SQ KF award reservation and later had my LH *G replace the KF# (only basic Blue tier) to get lounge access and extra luggage allowance granted. No problem. Agreed there is no mileage credit involved in that example but the concept of switching FFPs on check in is still valid.