Paul, I don't think it is at all clear that correcting the float height is going to make a big difference, given the rather diverse symptoms you have reported, but a greater float height does richen the mixture slightly. However the chonda tuning may be different from original Honda tuning, and the float height difference is fairly small anyway. You said that you have a spare jet that fits this carburetor. You have also said that applying a small amount of choke makes the engine run properly. If you don't mind using up your spare jet, I suggest you drill it out very slightly, and don't change the float height, or the original main jet. The problem is to find the right sized drill bit. You said a 0.97 mm drill bit fits through the original jet. You also said that it was actually a 1 mm drill bit, but measured 0.97 mm. Unless something really odd has happened to that drill bit, I'd suspect your vernier caliper of inaccuracy rather than the drill bit.
My normal approach at this stage would be to try a 0.95 mm jet drill bit in the jet. If it drops through, I'd try a 1.0 mm jet drill bit. If that dropped through as well, the next jet drill bit in my standard set is .12 mm, which is rather a large jump. Living in Melbourne as I do, I'd drive to my nearest industrial tools outlet and buy a 1.1 mm drill bit. I don't know how practical that would be in your part of the world. For reference, the first production GXV390 engines had a 0.95 mm main jet; all other versions had 0.92 mm, including the California-certified version, so it would not seem very surprising if the chonda version, with a different brand of carburetor, had a slightly larger jet. As long as you are working with a spare jet, not your original one, drilling it out to 1.1 mm as an experiment does not seem outlandish to me.
Before you do that though, had your carburetor ever been apart before you cleaned it? If it had, please inspect the tip of the emulsifier and if possible photograph it. If the tip is damaged, or the emulsifier is not quite seating all the way into the carburetor body, major effects on mixture might be the result.
