I guess I should have replied earlier, but here goes.
If the gizmo doesn't need to do anything else when it's putting out the frequency of choice, then what I've been working on may be of some value. On a mothballed project that I will call a guitar tuner, I have some arithmetic subroutines that convert chosen frequency into a scaler value which is repetitively added to a 24 bit sum. The top eight bits are then used to fetch a value from a table, which is fed to an output port. An input pin is checked to determine if the halt button has been pressed, and failing that the cycle repeats at adding the scaler to the sum.
At a clock speed of 4MHz I can get just over 10kHz output, but not by much. The DAC (R2R ladder) is external to the uC.