It would be so cool to test immediatly with real hardware, but sometimes simulation can also show a lot. The use of weaver for SDR CW demodulation should be very simple, but let see:

Created in no time, SDR simulation with Delphi and Mitov Signal Lab. Sample rate is set to 25msps, input signal is around 3.51mhz, LO is set to produce 600Hz tone. Seems to work! What I did not manage in "no time" was to find a way to change sample rate with the mitov components, so the Audio output with very small bandwidth is still sampled at 25mhz, so only small part of the waveform can be seen in the upper scope view.