My take on that report is that the mylar diaphragm alone works correctly, but you have now adjusted the metering lever height, in the metering chamber where you had already replaced the diaphragm. If you have done that, it changes the air/fuel ratio of the carburetor. However, you report that it now runs fairly well, so you may have only made a small adjustment (the metering lever height is a rather sensitive adjustment).

Here is the Walbro service manual for your carburetor:
http://wem.walbro.com/distributors/servicemanuals/WTseries.pdf

Please read the manual, paying particular attention to the metering chamber and the metering lever, then clear up a couple of points for me:
1. Did you change the metering lever height?
2. Does your carburetor have externally accessible H and L mixture screws?

If you post a picture or two showing the H and L screws, that will help also. Please do not make further adjustments to the metering lever or the H and L screws until we have these points clarified.