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[FRR]

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[TiN]

I maybe have one ADC but it need some parts (DG4xx switches and some JFET perhaps).

Also it's a bad idea to power on meter with open traces in that area, because that part of circuit is bootstrap capacitor multiplier supply. Chances are that now you killed bunch of opamps/parts in input front end which uses boostrapped +38/-38V supply to provide high impedance input that this meter have. 

[coromonadalix]

Not sure i would go all the way to remove parts, you may create more problems, i would focus on the remaining problems if there is, after a good cleanup.

You have good cleaning products who can go under the parts and do a very good cleaning.

At my job we use liquid flux who goes everywhere, we rince to board fully after in de-ioniozed hot water with Atron SP200 and or Atron AC205, it remove any greassy stuff and flux residues, and with air spray we remove any water excess and put it in an pcb dryer.

[Le_Bassiste]

I managed to acquire additional parts (including an adc board) needed for the project so making a bit of progress now. The PCB was repaired and all missing components have been soldered into place. Now was a good time to power up the unit and see where we are.

I have considered putting this into the ultrasonic cleaner, but I am not sure it will get everything out from under all of the SMD components.

well, unless you have definitive information on all exposed parts being suitable for ultrasonic cleaning, just don't do it.
as coromonadalix already said, proper (and repeated) cleaning will most likely do the trick. i can confirm that from my own repair experience on several stone-old 200x units.
patience is the key.

[TiN]

If that would be me, I'd go with desoldering/cleaning/soldering new components (not old ones! When not custom parts) path. With care and patience, it does not sound so bad. Also meter must need full recalibration anyway, so that doesn't matter anymore. 304.6/304.7 errors are often result of excessive board leakage, cleaning of ohms area and area around switches near LTC1043 may help on those.