Microwave oven rectifier diodes are overkill, they are huge at 22mm and if you have space then use them, but on a pc board I would fit the same size parts to maintain HV clearances. What kind of room do you have?
I would use fast recovery as higher current diodes are slower, the originals surely were lower current parts. Note the CL family is rated 450mA avg. IN OIL and "blank" recovery spec. HVM family has no recovery spec. it's slow.
Vishay GP-02 to 4kV 250mA and small 5mm, but slower 2usec trr. I get panasonic inverter microwave ovens out of the garbage and remove their fast recovery diodes, used to be Sanken UX-C2B. RP1H is 2kV 100mA 100nsec trr 7.2mm
20uF at 3.2kV is huge. Are you sure about that? I think the doubler caps must be small ceramics and end up limiting the current, with a big 20uF as the final filter cap?
Suggest
Ohmite OX/OY series HV resistors for inrush.
Ceramic capacitors actually age, I would check the multiplier caps (without them arcing to your multimeter, discharge them all first). Modern ceramics are not as good, the cheapies from china on eBay have a huge voltage coefficient and end up less than 1/2 rated capacitance at 1/2 voltage, so upsizing them is mandatory.