Since the eye bulge is perfectly spherical, why not use a cast modifier instead of warp. It’s faster and easier to setup. I picked this up from Helmut_S and i use it in many different places in my rigs ever since.
The Test below maybe a tad to overexaggerated (put this together in 5 min) but you can be quite suttle and precise with it, have a look…
EyeBulgeTest.blend (648.6 KB)