At the very least, I think southern peas (black-eyed peas, purple hull pink eye peas, lady peas, zipper peas, crowder peas, lady peas, etc.) would grow great in only west sun and they aren't picky about the soil either.

Okra also thrives in a western exposure.

I also grow winter squash, cucumbers, Armenian cucumbers and watermelons in an area where they are sort of shaded in the morning and then in full sun all afternoon and all evening until just before sunset. They do great there.