Yes, at some point, the low fuel level just can't keep up with demand.
Back to the spring loaded float needle. It is really easy to do this incorrectly. Did you hold the carb on its side while adjusting? If you held it completely upside down (vertical, the most reasonable people would do it) I guarantee you it is now set incorrectly. The weight of the float is enough to compress the spring in the float needle, giving you an incorrect measurement. The float level must be set with the carb on its side so that the float just barely kisses the needle.
Like x1rcr said, the clear tube method of checking your fuel level works great. Do this with the carb still installed. Just connect a 1/8' dia piece of clear tubing (you might have one on it already) to the overflow outlet on the bottom of the bowl. Hold it up in a loop next to the float bowl and loosen the screw for the bowl drain, next to the overflow outlet. Fuel will flow out and the level in the tube will equalize with the level in the bowl. It should be about a 1/16th to 1/8th" ABOVE the float bowl gasket surface.