The loss of sheen is actually sort of reassuring. To me it indicates that you don't have a shellacked finish, but rather, wax.
That's a big plus in my book. Any time you want to restore the sheen, just re-wax it. Lacquer finishes of various types are
often used to cover lousy sanding jobs and ugly fills.
I've had the stain come off on my hands with a Ser Jacopo. You can try rubbing it with a cloth and whatever solvent seems
to work best -- to the extent that you want to remove any excess stain -- but you're taking chances with the ultimate
appearance of the finish. In my case, with a $250+ pipe, I had the nerve to use alcohol and it worked beautifully!
But that was admittedly taking quite a chance. You might be better off exercising some patience as the weeping stain will
probably stop.