Wasn't there a build a few years back where the owner adapted the pineapple clamp sprocket for the engine by bolting it directly to the Fixie's fixed sprocket?
Had to drop by and see what you are doing. I used a w mart fixie. Its the common double diamond frame just what the CG was designed to fit. If you have an 18t fixed sprocket on a flip hub the common CG 9 hole sprocket will bolt perfectly to it.
The bike I built is the one with the 3spd fixie hub as a trans. Started as a 700c I dropped it to 26".