A few more notes from the front. Having replaced all the caps on two units, I can safely say there's no point in touching the larger polyester-film ones. The only ones gone dodgy between my two boards was a 10uF 16V, and two of the 0.01uF 100V. The electrolytics were of course total toast (max 20nF charge on a 47uF cap...). Probably next thing I'll do to one of the units will be replacing all the ICs (~20EUR in parts) and the transistors (should be <10EUR).
Below is a list of all the caps, just for reference (since MT's post is gone).
Polyester-film (10% tolerance)
1x 10uF 63V "big Bertha" 
3x 100nF 250V
4x 150nF 100V
1x 100nF 100V (axial)
1x 1.5uF 25V
2x 2.2uF 35V
1x 15uF 10V
1x 100nF 100V
1x 4.7uF 10V
1x 10uF 16V
1x 47nF 160V
2x 4700pF 400V
2x 10nF 100V
Ceramic
2x 68pF
Electrolytics
2x 47uF 16V
1x 4.7uF 10V
1x 2.2uf 35v
-----------------------------
Other polarized caps:
1x 2.2uF 35V
1x 1.5uF 25V
1x 10uF 16V
First repair attempt was to replace the electrolytics above and C19 (circled in green on the picture). Unfortunately it didn't work. Same problem: speed doesn't set. Pushing 'resume' on the stalk does hold speed but only as long as it's held.
I did notice something interesting though. There seem to be 3 other polarized caps, at least on my board, C9 1.5uf, C4 2.2uf and C18 10uf (circled in red on the picture). Polarity is indicated on the caps themselves as well as the back of the board. I edited the parts list above accordingly. Interestingly however, the schematic only indicates that C4 is polarized!
Next step will be to try to test relays and replace the power transistor Q1 (which I already have). Depending on the result I'll likely replace those other polarized caps on principle. I'd likely go with tantalum caps unless somebody thinks that's a bad idea. Comments welcome of course! Thanks and cheers,