I suppose because a couple of joists are lower, in my subfloor there is a 2' wide gully as much as 3/8" deep, running the length of the house, perpendicular to how I will be laying my floor.

Wide pine will be glued and blind nailed.

Shim with shingles? felt or sheet vinyl? leveling compound?

If either of the first two, do I glue it down, nail it down or both or neither? If I use shingles, how much gappage can I get away with in and around the shingles?

If compound, I assume I can't nail through it.

Thanks in advance!

In your situation, my preference would be to use wood shingles/shakes, well glued and stapled/nailed. Then sand smooth and even (flat) to the surrounding areas.

That's correct, IMO. Supposedly, there are some levelers that can be nailed into but I do not know which ones. Perry?

You can get a nail thru Ardex SD-F, without it busting and cracking out. It is the only one I trust to do so. It is like cement, with rubber.

Luan for the big dips...then feather out with shingles and felt.