That's an interesting idea. I assume caps are mounted on stationary frame and electrically feed to rotating rotor thru slip rings.
I don;t know details of how these cap "regulated" gens operate. I ASSUME the rotor windings generate AC that's rectified to DC by diodes mounted on shaft then stored in cap to power that rotor. Sounds bit like a catch 22 situation but from looking at schematic I'm GUESSING that's how it works.
If it were me I'ld try disconnecting the diodes and cap, connect rotor winding directly to slip rings ( make sure they are not grounded) . And try feeding slip rings ~ 6 or 12V DC and see what gen output voltage is and sine wave looks like.
If sine wave looks reasonably clean, they have universal Ac voltage regs for gens to automatically supply correct rotor excitation to maintain 120VAC output . The guys on Smokstak.com like to use $20 cheap China clones of SX460 reg. https://www.ebay.com/itm/AVR-SX460-Automatic-Voltage-Volt-Regulator-Replacement-For-Stamford-Generator/252854101446?epid=3017474321&hash=item3adf4765c6:g:eR8AAOSwU8hY6yfx:rk:3:pf:0
It senses and is powered by 120VAC output , it feeds rotor with excitation voltage. Min rotor ohms is 15 ohms, but if rotor is lower than that just add series resistor. It also has limits on how high or low it's excitation voltage can be , but that's easy to check by experiment ( test what DC rotor voltage it takes to output 120VAC, variable DC power supply or gel cells in series).