Only THREE things I can think of to cause this problem: Delivery pressure too high, a blocked float chamber vent tube... and you've checked the float height and needle/seat to rule 'em out, right? Yeah, I know, that's four. Mia culpa. But that's th' lot, AFAIK.
That thing is a "demand" carburetter: only gets as much fuel as the vacuum in the intake will allow (in essence) into the top chamber over the diaphragm (or piston), raising the progressively narrower needle out from the jet orifice. That jet hole at the point where the air/fuel is mixed (the top) is almost the same I.D. as the size of the needle's O.D. at its shank. The delivery is regulated by the amount of fuel (level) in the bowl, and should when operating properly be somewhere over half way up the jet tube. The float needle and seat should keep that level with the fuel pump on, engine not running. Even without a jet in the tube, that level should not be higher, much less pour gas out the carb inlet. If it passes this "static" test, you've ruled out pressure, float/needle/seat as an issue.
The problem you seem to be describing is with delivery. Either pump pressure is too high, or the float/needle/seat not working properly (or maladjusted). If the fuel *only* pours out as the engine is running (as you've stated), THEN the vent tube will be a "likely suspect" as well. I'd also say: if you have anything other than an SU pump, I'd put a pressure regulator in the supply line between the filter and the carb. Most auto parts houses have an adjustable one on the shelf. Set it low (2~3 lb/sq") and you'll be sure of what the problem is *not*.
Hope this helps "narrow" the possible list of causes, sorry if some of it is redundant.