That's the same kind of failure I had. The fuse holder clips get loose over time and that creates a high resistance, which makes heat, which melts things. Yes, drill the heads off the plastic "rivets" that hold the back cover on, then you can pry the guts out of the J-box. If the circuit board is not damaged, you will want to reflow the solder on the circuit board connections, pull all of the fuse clips off of their terminals on the board, and give them a little squeeze with some small needle-nose pliers to tighten them up. Make sure when you push them back on that they are tight on both ends, the circuit board terminal and the fuse end.
Your in-line fuse by-pass fix should work fine if that's what you need to do.
Pic below of the circuit board out of the box, you can see the heat damage.