The real trick would be to buy the Paramount Soft-Start kit and put it in the Paramour II. The issue will be the available voltage, which is quite a bit lower.
The Soft-Start kit regulates to 300V, and you have 320V of B+ available. This may work just fine right out of the box, but if you happen to have significantly less than 310V of B+, the 149K resistors can be changed to 143K to give yourself more compliance.
This upgrade would give you the sonic benefits of the driver stage available in the Paramount.
If you want to rewire the socket for half a 5670, this is also possible. You can leave the C4S board set as-is, but replace the LED at the cathode with a 1.1K resistor. Do be aware that the 5670 has a very odd pinout (it actually looks beautiful and straightforward on the datasheet), so you'll want a fresh socket.