The circuit now looks like this:
The two outputs show the mixed down frequencies when the local oscillator is tuned to its two extremes.
The lowest frequency is about 13kHz, which is probably a bit high. But let's wait until we can listen to the signal until we fine tune it some more.
The next step will be to define a push/pull amplifier for the loudspeaker. By the way, a loudspeaker might draw a bit to much power, so I'll see if I can use a summer from a PC motherboard instead. I'll need to measure its impedance first, to make the calculations for the amplifier.