I find it difficult to answer because:
There doesn't appear to be a choke as such. There is a two-position manual control connected to the fan-operated speed governor (but not to the carburetor itself) by a large spring. I keep this in what I assume is the "run" position at all times because the engine slows or stops if I move it into the other position. The engine starts with only one or two pulls on the starter when primed by a few squirts from the bulb, and the manual control never needs to be used.
I can't report on any possible float chamber, because the carburetor sits largely submerged in the fuel tank, and I didn't have the time to remove it to examine what lies in the tank. I shall try to do this next weekend.
In the meantime, I had some photos taken (by my daughter, who e-mailed them to me) to show the carburetor and control configuration, and I shall try to attach them to this reply in case they help with your diagnosis.
PS:Sorry, I can't send the photos with this reply because I can't seem to convert them to a format acceptable to your system, so I shall send this answer anyway. It would help if you could send me a direct e-mail account so that I can simply forward my daughter's original e-mailed versions. In the meantime I shall try to convert them off-line.
In the meantime, any further advice from you would be welcome.