> Would have dipping the whole sewing cabinet been better at cleaning
> out the grain?

Dipping is the surest way to completely destroy a piece of furniture.

Never, never, never dip strip anything. Among other things in your case
dip stripping will allow the stripper to penetrate and dissolve the glue
that affixes the veneer -- bye-bye veneer.

I don't think there's anything for it but a lot of time spent with a
fine brass brush and elbow grease.

Mike in Sacto