I've started on what I could of this design based on some old papers and what I could understand of electrometer designs as someone who doesn't work with tubes.
The basic idea is referencing The Application of the FP-54 Pliotron to Atomic Disintegration-Studies by L. R. HAFSTAD and A STUDY OF ELECTRONIC METHODS FOR THE MEASUREMENT OF SMALL DIRECT CURRENTS Technical Report to The Office of Naval Research under Contract No. Nonr 580(00)580(01), AD15894 using a one tube circuit based on the one used in the atomic disintegration studies with multiple ranges added.
There they had to coat the tube in aquadag, float the grid and work with the rate of drift to measure tiny currents with a time constant of ~300 seconds.
For the basic circuit I just took the idea of the regular one-tube electrometer circuit and put in a reed relay to float the grid and a set of reed relays and high value resistors that can be switched in and out on the input side for the current measurements.
The papers mention countable values of electrons and with statistics being way in the past for me, if I use a modern precision digitizer on the output (of some sort) and use the ability of a computer to do statistics and regression analysis shouldn't that be able to chase down to attoamps without shot noise playing a huge factor, especially when factored over a 5+ minute measurement time minimum? Especially since instead of batteries it would be possible to use a more modern power supply with high isolation values and lower noise than a battery in the sub 10Hz range especially.
For voltage, I take it I'd change the anode resistor to vary the amplification factor of the circuit?
The only one that has me truly stumped is integrating charge for measuring C and how such a circuit would be implemented.
This idea is mostly just to work on a ridiculous idea and design, analyze, and mock up in CAD a ridiculous circuit that borders on "gives a warm fuzzy feeling just from getting it to hypothetically work" since wheeling around a table with a UHV chamber of resistors and magnetically shielded vacuum tubes with a 4u rack of the control and interface electronics is not practical currently.