Other than the water base latex, if I recall, one of the main problems with most of the other finishes, is that the solvents will also dissolve the pitch, except the alcohol. I would imagine that epoxy might be a good option, except I'm not sure how good the adhesion would be.
Not knowing what grade of pine you started with, but some of the lower grades at the lumber yards are only dried down to about 20% MC, which may or may not have been in a kiln. It's been a while since I read something about this, but there are a number of compounds in this rich-pine that liquify at different temperatures. Some will flash off at a low temp, while others have to get on up there. If your shutters are painted dark, and out in the full afternoon Sun, that temperature can get quite high, so it just melts.