I'd say you could easily get 3600 with a 22-243AI with an 80 grain bullet. My 22-250AI gets 3500 with 80 Amax bullets. It's not a hot load either. The 243 AI case has more case capacity. Not saying it would be the most accurate load but my 3550 fps load IS my most accurate in that rifle.The E-Z button would be a straight forward 22-243 in a fast twist tube. When I was shooting a non-AI version, I simply ran Lapua 243 cases into a FL 22-243 die and went shooting. But, you won't get to 3,600+ with a heavy bullet. IIRC, I was getting around 3,400 ft/sec with a Berger 80gr bullet in my 22-243 (plain).
I might add that I had surprisingly good barrel life with my 22-243AI. I put 1,000 rounds through the barrel before it was set back and rechambered to 22-243 (plain). It shot almost as good as new again.