I still say it does not matter but to cover a few points more specifically,

"Ken McIsaac" wrote in message
...

Would you recommend drilling before applying the poly or after? If I
drill before, I can see the poly dripping into the hole and needing to
be drilled or scraped out, which will probably mar the finish around
the hole.

If you drill and use pencil marks or similar marks to mark the location and
do this in the wrong place, it is easier repaired before the finish goes on.
You can resand after drilling the holes to remove marks or sand down the
repair. Dont worry about the finish gettin in to the hole. The finesh is
going to remain relative soft for weeks and even then a decent drill bit
will cut the finish if you need to resize the hole.


If I drill after, then I am drilling through a thin film of plastic on
top of the drawer face, which I can imagine might crack or spider-web
or something.


I have done a lot or repairs and modifications to pieces with finishes that
are years old, I have never witnessed any checking or spider-web or
something. You are not drilling through glass. ;~)


Which is the least error-prone way to do this?

The least error-prone way is the one that you use that works best for you.
Typically the way that is the easiest to repair should you make a mistake is
to drill the holes first, finish, resize holes if necessary and attach
pulls.