If rinsing the piece is doing the trick it could be that your enamel
was contaminated indeed. It is always a good idea to rinse any piece
before firing. Using baking soda and rinsing well helps remove acid
and other contaminating substances.
As for solder, if you were to use IT solder ( or maybe even hard
sold= er) and protected the solder joint with yellow ochre, graphite
or water based white out your solder joint should not get pitted.
Maybe it is worth atry. You are brave, I would not solder a piece
after it was enameled.