3 year-old biting finger nails

Anyone in the group have experience dealing with a young nail biter? My son
has been doing this for a couple of months now, and I am looking for more
ideas to help him stop. We have tried the positive reinforcement route - a
small treat in the evening if he hasn't bitten his nails that day - which
has only worked on random days (so I guess it hasn't really worked We
have tried explaining that his fingers are dirty and he might get sick, and
we've tried giving him small things to play with in the car or while reading
on the couch to keep his hands occupied, all to know avail. We haven't yet
tried the nasty tasting stuff you can put on fingernails - my son is great
about washing his hands every time he uses the bathroom, so I don't know how
well it would stay on, anyway.

The Amer. Academy of Pediatrics has an article that says to ignore it and it
will eventually go away, but my parents did that for me and I bit my nails
until I was 32. I wouldn't have any huge objection to it, except that he
bites them down so far sometimes that they get sore - he isn't making the
connection, though, that he made them sore by his own actions and can
therefore make them better by not biting. At what age can they reason that
kind of thing out, anyway?

He also picks his nose a lot, but most kids his age I know do, too, so I
don't know if that is related or not.

Just wondering what worked (or didn't) for others.

Kat