The movement is 200 microamps, and the numbers are linear on the dial (except for ohms), so I assume the transistors need to be linear in the range used.
Is either or both linear below 200 microamps?
I think that your understanding of the operation of the FETs in this circuit is not quite correct.
They are configured as a basic differential amplifier.
The 200uA meter is connected between the sources of the two FETs.
My best estimate is that the FETs will be conducting around 6 or 7 mA during normal operation when the meter is reading zero.
When reading full scale, the diff-amp will be unbalanced so that there is about a 1 volt difference between the sources of the two FETs, causing 200uA to flow through the meter movement.
The FETs themselves are always conducting more than 200uA, so linearity in that area and below is not a problem.
So, I suggest the you buy some FETs, J112 or J201, or 2N3819 if you like.
As suggested by schmitt trigger, if you buy more that two FETs, you could try matching them, I don't know how critical a matched pair is in this circuit.
**Idea**
It is possible to buy two matched FETs in one package, you could try that approach, but it may be a bit of overkill for this application. (Sorry but I dont know any numbers for matched FETs just off the top of my head).
JimB