I have no idea if any of Oliver's BG changes were actually caused by his DIET changes but you can check out his spreadsheet and read about his numerous changes. After being diagnosed he stayed on Kirkland dry food for 2 weeks, then switched (per vet orders) to Royal Canin Glycobalance. But I took him off the RC Glycobalance (which seemed to raise his BG!) and switched to Fancy Feast (which clearly lowered his BG).
I later added some Friskies for snacks but saw a possible change in the duration of his Vetsulin. The Friskies has rice in it. Wanting to keep things simple, I omitted the Friskies and am feeding him only FF.
None of this may be scientifically valid but that's all I know, for what it's worth.