Update: losing that mission was the best thing I ever did in Skyhammer.

Once it started assigning me new missions, I was able to take out the remaining 3-4 unowned sectors rapidly, and now I've advanced to the second city without having to use any cheats! Very cool and satisfying to make it this far, when I had been stalled on that one mission for several months.
The only problem I experienced was that when I finally lost Sector 10, the game got a bit confused about the state of that sector, and would sometimes assign both missions to take it out. The game crashed on me several times when I got too close to the node as a result, but I could move around and complete missions in other sectors, save my progress, etc. with no problems. So here's the workaround I came up with, in case somebody reading this hits a similar "double mission" problem:
Get as close to the node as you can without locking up the game. You probably won't see it on the screen, but it will be in the short range radar. Use a smart bomb (A+B+C) to wipe out everything, and the mission will be completed.
I wish the difficulty was a little lower on Skyhammer, because it's hard to imagine I'll ever make it to the end of the third (!) city, but it's still a blast to play.

For anyone who hasn't made it very far, there
is more enemy and mission variety the longer you play. Near the end of the first city, I was often fighting Advanced Drones (tougher than the dime-a-dozen Drones you see flying around), Spys (look like UFOs, and
amazingly fast), and the floating Gunships (watch out for their endless missile volley!).