Re: wrap deformer creating unexpected bulge

it should get better as the grid size goes down not up. There is something odd about your spline. Try changing the spline Intermediate Points to Subdivided and set Maximum Length to the same value as the Regular Grid size. (make both be 10 or smaller)
It may (but shouldn't) help to pull the Wrap out of the extrude and group it in a Null with the Extrude like this

+Null
-Wrap
+Extrude
-spline

if that doesn't help I'd have to see the scene file.