The book shows that the BSE 440T that came in that model produced about 33 horsepower and used a Walbro WD-B30 carb. This carb is a diaphragm type with an integral pulse operated fuel pump (hence the diaphragm).
I have rebuilt a number of these units in the past and they are real simple and easy, they just have a lot of layers as you have seen. Take great care when you put it back together to get every thing in the right place, and the screws torqued evenly. Tight but not too tight. It is a good idea to actually replace the diaphragms whenever you take them apart. You can get a complete kit for $10 - $12 bucks or so.
- Make sure all of the diaphragms are below their respective gaskets (including the one in the fuel circuit plate). This is the somewhat rectangular removable plate you can see after you take all of the other plates off.
- Make sure check valve tabs are properly closing off the fuel passages. If not you may have the diaphragm upside down.
- Make sure the springs, check valve, and leaf spring (that funny flat piece of alum.) are all in position.
- Check the needle valve and seat to ensure that it is clean and in good condition to make a good shutoff for the gas.
- The metering lever should be .005 - .020 inch above the surface of the carb body with the carb in an inverted position and the lever resting on the needle valve. In other words a straightedge should just barely deflect the lever when slid across the body. You simply bend the lever to adjust, just don't put any pressure on the needle.
My guess is that you may have a problem with #4 or #5 above. If the metering lever is high, or the needle valve leaks, or the rubber check valve is failing, or the pump diaphragm is leaking it can supply too much fuel.
I would get a complete rebuild kit (Dennis Kirk, Shade Tree, Rec Leisure, etc.) and replace all of the gaskets, diaphragms, springs, check balls, check valve, leaf spring and needle valve.
On another note, problems with this carb are usually lack of gas, not too much gas. I guess this is good news.
Sorry so long, but thought something in here might help.