Program one of the general purpose counters on your 6070E to perform retriggerable pulse generation triggered off the encoder signal. Program the other general purpose counter to perform gated pulse train generation (use output of first counter as gating signal). Adjust pulse specs of second counter on the fly using Counter Control - switch cycle. Feed output of second counter to PFI5 (or a RTSI line) to drive analog outputs.
Stick AO Single Update - output only in your loop to poke new analog values onto the board. Anchor you SW loop frequency to the output signal of your second counter with Counter Control - wait (supported on RT only).
So your VI should configure one counter for retrig pulse generation, another for gated pulse train, and HW-timed singl
e-point AO. In the loop, call Counter Control - wait to wait on pulse train output, followed by AO SingleUpdate - output only, followed by Counter Control - switch cycle to update freq of pulse train if necessary.
Adjust length of the retrig pulse so that you get enough pulses to output all 6 sine waves. I *think* you can use switch cycle on the retrig counter. If so, you can adjust phase relation too.