To answer my own post, I called a couple more times, and was again told that I run the risk of losing my confirmed seat on SQ even the attempt is made to separate the PNR.
The agents indicated that it probably would not be a problem, but since they know how difficult SQ F/J awards are to secure, and that there is currently no more SQ award inventory available on my flights, they want me to be aware of the risks in advance.
I decided not to chance it, and just leave my PNR the way they are. However, I did learn that in the future, I would always put each of us on a separate PNR for award travels.