Daniel,
I have this generator and have experimented with it. You could add AM modulation by using for example an Analog device AD734AN 4 quadrant analog multiplier IC on an extra board added inside. The FY3200 series has plenty of room inside for an extra circuit board and more than likely plenty of power from the +/-12V internal supply.
However, without interfacing into and changing the FPGA code you won't be able to do FM modulation.
gby