Viet_Cong, don't worry about one part of the tube being larger than another. Remember, when you observed the "anomaly", you needed to inflate the tube outside the tire, which means that the air inside the tube is working against the rubber of the tube only (and atmospheric pressure). This isn't much resistance and you can verify this if you measure the air pressure inside the tube and see that only a couple of psi will result in massive tube deformation.

Once you install the tube inside the tire, you typically have to pump up to several dozen psi of pressure to make the wheel useful. Most of this pressure is held by the tire as you've already verified that the tube can only hold one or two psi at most. The tube really offers minimal resistance and only acts as an air barrier in the entire tire/tube system.

Due to this lopsided distribution of resistance, the anomaly in the tube ceases to be an issue once you get the wheel up to operating pressure.