Well I have a non-working 335D at your disposal, if it will help.
My thoughts in no particular order:
Use a modern chopper, ala Conrad Hoffman's mini-metrology lab (modernize to use an OPA189).
Perhaps you can replace the neon with a modern optocoupler like the H11F1M
You can get mosfets with a substrate lead from LS (Linear Systems) e.g. http://www.linearsystems.com/lsdata/datasheets/SD5000%205001%205400%205401%20QUAD%20N-CHANNEL%20LATERAL%20DMOS%20SWITCH%20ZENER%20PROTECTED.pdf
I have a couple of SD5000, I think, if you need one at cost (they are expensive).
I know that the existing ckt works if the choppers work so I'm starting out looking to replace the minimum amount of circutry as inexpensivly as possible.
One of the replacements that I looked at hinted at problems with the ±15V supply so I'm also trying to minimize changes there. Measurements that I took when I replaced DS1, showed that the PS on the detector board was +12.8, -16.8. The + supply was 15% low & the - supply was 2.5% more than spec'ed. The - ps is probably OK. My notes say that C3, 4 were previously replaced and have acceptable ESR & capacitance. I will check them when I open the beast.
The output waveform of the transformer low voltage winding is a not too bad square wave. (Newfile4.png)
I have a few shots of the neon ckt waveforms. I measured R2 (31.25kΩ) and used it as a shunt to get an idea of the neon currents. Newfile 9.png has Ch 1 at the node R2 to CR3, 4 and Ch 2 is at R2 to C1. Math waveform calculates (CH2-CH1)/31.25e+3. The RMS current is about 1mA. (I'm not sure how good the RMS calc is for that waveform.) The neon voltages (+ diode drop) are about 75V.
The output from the HV winding is also a square wave (Newfile 12.png) about 225Vpp. Ch 1 is on pin 1 of the card and Ch 2 is on the C1, R2 node. Math calculates the voltage across C1.
I figure that I can add about 6mA to the low voltage winding for every 1mA I eliminate from the high voltage winding without changing the primary current. I don't know much else about the transformer except that it's sealed, probably potted and about as high on the unobtainium scale as possible if I 'break' it.
The neon current is about 1mA so my 'budget' for the low voltage winding is 6mA give or take depending on what happens to the voltage.
I'll look into the H11F3M which doesn't have problems with charge injection. If the PS will tolerate 3 to 5mA it's probably the way to go.
Also, thanks for the offer of parts. Do you know what is wrong with your unit?