2x 0.18uf 450V metallized polypropylene caps - these are in the shunt regulator stability bypass RC network, and may have some effect. It will be very small though! They must have good high-frequency behavior, as in VHF radio frequencies - so forget mylar. In polypropylene, look for film and foil, or anything labelled "snubber". AC line rated ceramics may be a good choice.
2x 10uf 250V metallized polypropylene caps (Solen) - these are the parafeed output caps, and by far the most important sonically. Look in the power amp sub-forums to see what others have used in that function. Whatever you try, remember that breakin is especially audible with these caps, it will take usually 50-200 hours of actual, loud, music before you really know what they sound like.
3x 220uf 250V electrolytic caps - these are in the high voltage power supply, isolated from the audio by two C4Ss and a shunt regulator, and not going to be directly audible. There are two areas for possible improvement - you can look for caps of higher temperature rating (105 degrees C) and higher voltage (up to 450v) which will help the caps live longer, and you can bypass them in the hope that it will reduce switching noise at radio frequencies. For the latter, snubbers and AC line rated ceramics are good candidates.
*** for switching noise, consider replacing the UF4007 rectifiers with Cree silicon carbide Schottky diodes, 600v or greater; that will likely make more difference than bypassing the filter caps. ***
2x 10,000uf 6.3V electrolytic caps - these are "soft-start" time delay caps; their AC behavior is shunted by the LEDs so they are unlikely to have much sonic effect. Also, the location is pretty tight; the extended wires necessary to use any alternative would probably do more harm than any possible good.
1x 10,000uf 10V electrolytic cap - this is the heater power filter, not connected to any audio area. It already has Schottky rectifiers, so the least unlikely improvement would be a bypass for high frequencies. Low voltage ceramics in Z5U material would be a good candidate. I'd want 10uF at least to have any possible effect, and note that these caps lose a lot of their capacitance with DC voltage on them - use 16v or 25v parts, and you'll probably want the 22uF or greater nominal capacitance.