I thought I'd ask this here because you guys are all used to the care and feeding of high-grade side-lock guns ,

This is not such a high-grade gun, but it is worth rescuing from a careless lack of love, An L.C. Smith double-12 that someone at some point over-ran varnish onto the metal. The metal is in good shape with echoes of the case-colors still present.

How to best remove the varnish overruns without affecting the metal finish?

I would very carefully use Qtips and lacquer thinner.
Phil

Ditto, in addition to removing the butt stock to eliminate any chance of intruding on the wood finish.

I used lacquer thinner on a Savage 99 that was coated in cosmoline didn't hurt the blue at all.

Thank You Gentlemen, I will proceed with lacquer thinner.

Any thoughts/trix on reviving the remaining case color contrast ?

Nothing to be done there, short of polishing everything and sending it out for re-color case hardening.

Acetone or Jasco - shouldn't bother the case coloring as that comes from heat not chemical reaction.