The PJCCS does not keep the current constant, it reduces the current in proportion to the battery voltage. It also adjusts the bias voltage in the same proportion, since that current flows through the bias resistor. This way the plate voltage is maintained at about the same proportion of the battery voltage so the circuit continues to operate throughout the battery life.
If you wanted an LED bias, you could add one or two 9-v batteries and use a regular C4S current source. The extra batteries are needed to keep the C4S input voltage well above the plate voltage as the batteries fade out.
A reasonable alternative to extra batteries is to use NiCd or NiMH batteries, which have a relatively flat discharge. Unfortunately, many of them run low, like 7.2v, and you'd want the full 36v - so you are back at five "9-v" batteries - or a custom battery pack and associated charger. Starting to get complicated now...
