Does it (stereo encoder) really work???

Yes, it was you, Audioguru who brought me back. Glad to see you posts again.

If you use capacitors that are stable with temperature like silver mica your osc will be reasonably stable.
As a rough and ready way you could hand tune the 38kc and 19kc source by hand while looking at the stereo indicator on your radio, or do it on 2 or 3 radio's to minimise the difference error.