Way more simple, if you have access to the baseband signal, is to trigger on the demodulated signal using another channel or ext. trigger input.
Right. This is blindingly obvious in retrospect, and works perfectly, within the slightly clunky limits of the UI of the FY6800.
Thanks.
For those who are interested:
The FY6800 has two o/p channels, and allows modulation of CH1 by CH2 (or by an external signal). So you can use CH1 as carrier and CH2 as baseband.
However, you can only adjust the modulation index in real-time while seeing the changes on the scope; if you want to change either CH1 or CH2 freq., the device stops generating the modulated signal, but reverts to the control page for CH1 or CH2 - this means that you have to change those frequencies blindly, and go back to the modulation page to see the effect.
[edit: oops! I got this wrong - the modulation page in fact allows you to modify the freq. or amplitude of the CH1 signal - you can't however modify the CH2 signal on that page, AFAICS)]
I assume the fancy Rigol and Siglent generators are more flexible that way, but for the price of the FY6800, I wouldn't want to complain (too much...)