You probably find that if you do the pop off pressure test I suggested, you will find that there is a slow leak at float needle valve and seat. A good seal at this area must maintain least 5 psi of pressure with the carburetor inverted and just the weight of the float holding the valve closed.
I have seen seats where a hairline imperfection would leak. I mean one that I had to magnify to even see but my eyesight isn't the best either @ 58. It take time the float bowl to overfill which why a quick test doesn't show up the problem as this a seepage problem. Need patience to fix this one.
First you install a new needle and re-test. If it then fails the pressure test then it is the seat. Sometimes a little polishing compound works and cotton swab but most times they need a new seat. When you to get to this level it is time for a replacement carburetor as the Honda carburetors don't have replacement seats available.
