I thought that when you pull the "plug" out, the pocket of air that escapes is from the pump itself and not the tube. Unless you're somehow pressing down on the "plug" to pull it out? The 60 psi reading might be from you pressing the "plug" back in. I think you might be doing this wrong somehow!

IMO, most hand pumps suck. I use a Specialized one that advertises "Up to 120 psi", but I think I need to work out more. 600 pumps = 80 psi. Beyond the first 600 pumps is another exercise in itself on a ride. Not exactly what you want in the middle of a 75 miler...