That is a conventional voltage doubler circuit. The two capacitors are charged alternately on the two opposite AC half-cycles, and discharge in series to give twice the DC output voltage compared to a conventional bridge rectifier albeit at lower current.
The existing selenium rectifiers can be replaced with ordinary silicon diodes but the HT might be somewhat higher than originally intended. The normal cure for this in selenium-to-silicon conversions is to add some series resistance to substitute for the resistance that was inherent in the selenium rectifiers, but whether it is actually necessary here depends on how great the drop originally was. Is there any indication of what the DC voltage should be, other than the absolute limit of the capacitor voltage rating?
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They look nice though! Maybe re-stuff them?
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They do look nice, but I would not re-stuff them. Partly because I now have a policy of preserving unusual vintage parts instead of mutilating them with drills and knives, and partly because if stuffed with a diode, they will have different characteristics which will conflict with what they claim to be (unlike a restuffed capacitor that is pretty similar to its original spec). I would put them in a little ziploc and tape it inside the bottom cover.
I have a similar-but-different chart recorder of the spark-trace type: A Farnboro engine indicator as developed by the RAE in the 1920s to study the combustion conditions inside the cylinders of aero engines.