What should I do about shingles that are stuck to the sheathing?
Here is what I ended up doing:

The entire roof had an ice and water shield that was sticking the shingles.  This guy's write-up about his roof closely mirrors my situation in that it was south facing, low slope, and old.

After deciding to just lay shingles onto the remaining old shingles, I noticed that the sun warmed up the substance to the point where it was relatively easy to peel off the stuck shingles with the roofer's spade.  So I got the old shingles off, put down felt and applied new roof.  Thanks!