We may have an answer.

I decided to switch Cole to a less expensive sensitive digestion food, by Iams.

I took some over to my mom's place to see what Binky thought.

He loves it! Even though he has few teeth, the pieces are small and he manages fine, just as he does with the Greenies digestive treats.

Mom also asked me to find a different brand of turkey and giblets as well as chicken-liver feast. I found them both in Max cat.

This is a cat who has been eating Fancy Feast and Friskies all his life and threw up a lot of the FF.

Fingers crossed that this works. It'll be easier on Mom and easier on Binky - how does one rehome a 16-year-ols Lilac Point who is totally bonded with one person?