As per my understanding, the extra bag allowance is attached to the student booking class (ex. Student Premium Economy Lite).

The dual FFP trick you mentioned works with United Airlines. I always book a student ticket and then get in touch through chat/call to change the FFP to my SQ KF #. As a result I always use my KFEG benefits on UA student fares and I credit to KF. Having said that, the FFP section is grayed out on the UA website so you're unable to change FFP online.

A quick search on SQ's website with my student booking yields similar results. I am unable to change my FFP online but I think it would work if I gave them a call/live chat or tried at the airport.

I am pretty sure the extra baggage allowance would still apply to your booking regardless of whether you credit to KF or another FFP. Having said that, while I am not 100% they would let you credit to another FFP I think it shouldn't be a problem.

I have purchased student fares with multiple airlines and I have never found it an issue to change my FFP. It's just impossible to do online.