All they are doing is acting as current sources (actually constant current sinks) to develop a bias voltage across D1,D2, and D3,D4 respectively to permit the output voltage to be adjusted right down to zero and also the current limit the same way.
A JFET's Idss is not a well defined parameter and its probable that the current would vary over something like a 2:1 ratio between different FETS with the same part number.
e.g:
A 2N3822's Idss is expected to be between 2mA and 10mA
A 2N5640's Idss is expected to be between 5ma and 15mA
Substitution by any other sort of current sink should work, as long as there is enough current to get the diodes above them conducting. I would avoid OPAMP based current sinks as you may run into stability or bandwidth problems.
A -12V bias supply gives you 2V extra headroom so a high gain NPN transistor with its base to a 2.7V Zener holding its base above the -ve bias supply with a pullup to 0V and an emitter resistor to set the current should work nicely. Both sources can share the same Zener and pullup resistor. Try 390R for the Q1 replacement's emitter resistor for just over 5mA current and 180R for the Q2 replacement for just over 11mA.
Performance may actually be better than with the JFETs, but be prepared to fiddle with the emitter resistor values to get zero current and zero voltage right at the end of the control pots' rotations. Maybe even use a 1K preset and a 470R preset. What you are doing if you make them adjustable, is setting the current through the two diodes associated with each of the original JFETs so that their total Vf matches the associated LM350's reference voltage. Some experimentation will be required.
200mA is a lot of current for meters - you probably should have gone LCD. Scratch-building a reliable isolated DC-DC converter for 200mA out at 5V is not so simple. I suggest either using the guts of a mains to 5V USB phone charger if you've got room to mount it safely or getting an off-the-shelf potted module, e.g.
http://uk.farnell.com/tracopower/tmh-1205s/converter-dc-dc-2w-5v-0-4a/dp/1007558