I had a similar issue on my 1965 Moke with a 848cc engine replacing the original fuel pump (that was sticking off quite often, I left the side cover off so I could whack it from time to time). I replaced the SU pump with a low pressure fuel pump from NAPA. Fuel would leak from the overflow so I used another HS2 carb, same issue with leaking so I bought two carb rebuild kits and fitted them to the carbs. Same issue with leaking. I bought and fitted a new SU pump and rebuild an kit I tested the original (1965) pump with the rebuild kit, NO LEAKING. My moral - use original fuel delivery and carburation parts!

Float needles are easily overcome by anything over approx. 4 psi. 

 

Years ago there was an issue with inlet needles and jets not having enough tolerance. With expansion, the needles would stick, usually in the open position, resulting in bowl overflow. Not sure about HS2, but I had the problem with a HIF 44. The carb would warm up after a drive and would not restart because the engine would flood when off. The bowl overflow, being higher than the top of the main jet resulted in the fuel level being above the tip of the jet. Fuel would casually flow out the jet, down the intake, into the cylinder(s) and eventually to the crankcase. I found that out the hard way: when prepping my Mini for winter storage, I'd run the engine to get stabilizer up into the car. On one occasion, the engine stalled out and would not restart. I pushed it into its resting place, finished the storage ritual and left it for spring. 

 

Come spring, I discovered that my oil level was really high and the oil smelled funny. It turned out the fuel tanks was nearly full for storage but had drained half-way by gravity. The inlet needle had not closed on cool-down or even to -20C. 

A new inlet needle didn't help. The solution was to file the edges of the needle off to improve tolerance. The needle is cross-shaped in cross-section, so there are 8 edges to dress. Not much - just to take the sharpness of the edges off. 

 

Before all this, I went through the fuel pressure scenario. I replaced the mechanical pump. I substituted mechanical pumping for electric with a pressure regulator. I wrapped tie engine bay fuel lines with insulation. I finally resorted to a proper SU electric pump. 

The attached photo shows insulated steel lines, a fuel filter, behind the filter a Holley pressure regulator complete with pressure gauge. All futile!

It has the original 850 engine, with a single HS2 SU carb. Starts and runs, but has a gas leak out the top of the float lid vent hole. So I lowered the float, a lot, no improvement, tried a different lid next, same problem both times. Have a new vibram needle valve (no lower gasket) and new lid gasket. I am now wondering about the fuel pressure possibly being too high, as I recently installed a new fuel pump. guess I need to put a pressure gauge in the line. Gas leaks out even if I don't start it, so it sort of looks like the float is not working to shut it off. Any ideas or suggestions? Puzzled...