I'm not too sure it would be from the fuel line from the fuel tank, could be, but I think you'd notice the issue at other times, not just cornering and it would take a few seconds to become apparent.
But, to check if this is an issue, temporarily fit a Tee Piece in to the fuel line right where it connects to the fuel bowl and fit a pressure gauge (with about 4 feet of hose!) to that so you can hang the gauge inside somewhere where you can see it. Go for a blast and check the pressure when the problem sets in. You'll soon see.
I'd suggest checking the Jet is 100% clear of any muck. You'll really need to remove the carb to check this properly. I recall having this same issue but only on Right Handers (with a HS4) and that's what that was. It could also be that you are 'reaching' the limitation of what a HS4 (or any HS carb) can do and you might be better off going to a HIF44.
I doubt that fitting float bowl extensions will help as you can't raise the fuel level in the bowl (if set correctly) without to flooding over and flowing continuously through the Jet.