Correct. It does not sit in the cup of the lever. It is pressed into the body of the master. Then you insert the pin. The pin sits between the lever and the piston. Yes, it is halfway down the pin. If you look at the parts diagram you can see some ridges in the pin. These ridges help to locate the pin in the rubber boot and help form a tight seal against the rubber.
Your issues sound opposite of what *should* happen. If you go smaller in bore diameter you get a softer lever, more lever travel to move the fluid, less fluid volume moved, more fluid pressure.
If you go larger (which you did by .005" so in effect, not much at all) you typically get a firmer lever, less lever travel to move the the fluid, more fluid volume, less fluid pressure.
Doesn't really make sense that the lever would take more travel and feel softer if the MC bore is larger by such a small amount. I would lean toward air in the system. Could be residual air from having a totally empty MC to start with, could be some sneaking in past the threads of the speed bleeders during the bleeding operation ( i have heard some people mention this), could be some air leaking in past the seals in either the calipers, or MC (doubtful but possible, they typically last a LONG time).
If you have a might vac, give that a shot, if not, and your using the speed bleeders try putting a little bit of grease or some sealant on the threads of them.