I've once had an itinerary with SQ and EK in the same booking.

At least when there are different airlines involved, I was able to attach different FF numbers to each flight (which may be easier since EK was not in an alliance). I managed this from EK's MMB.

In your case (as it's all QR) I'm going to guess that it will be notoriously difficult for you to achieve this. I am inclined to agree with your strategy to post-claim the points, however the only issue I can see with that is if QR/Virgin then ask for your PNR as part of the process, they may try to credit ALL those flights to their respective program. If the claim form is done for each flight you might be safe.