I find the water / detergent approach works fine,
providing the boards are
dried well afterwards. Usually I use a hairdryer to get the bulk of the water
out from beneath ICs and then leave to sit in the hot water tank cupboard for
a week or so. Never had a problem with this, but it doubtless depends on the
quality of the water used.
I'd definitely investigate using distilled water, especially for the final rinse.
For the air cleaner- a room model might be good because it would (hopefully) keep some
dust out of your machines.
For cleaning, you can build a rudimentary "dust and fume hood" (although it
doesn't work for fumes) out of a box and a vacuum.
I've seen this used at small businesses to control dust. Just pop the computer in the
box, turn on the vacuum, and blow away.
For cleaning effectiveness, once you've used a tank compressor you'll never want
anything else.