I totally understand, and relate to all your experiences. I learn't to cull mice when I was keeping snakes as a means to provide a reliable supply of food. It didn't help that I also had two owls that needed mice as well.
Anyway, one of my college lectures taught me how to cull adults using the manual method i.e. holding mouse by back of tails and hitting the back of its head on a sharp edge. This came with all the discussed issues, but out of all the methods I have had contact with (did not know how to make a gas chamber) this is the one that I still use, but rigid application of a set protocol means that I have not had any injured or messy mice in a very long time.
During the years that I have been involved with animal care I did manage to learn a couple of other methods that work well and may be easier for some people to use.
1. Adult mice, put on a ridged surface, something they can get a grip on like a towel. hold the base of the tail and put a pencil over the back of the neck, push down, and pull on the tail till you feel the neck break. This method is effective and used in the labs alot.
2. Pinkies, upto about 8-9 days only, Pinch the back of the skull, causing instant brain trauma and death, never fails and it is the only way that I can kill pinkies and early fluffs now.
As to the lousy feeling after culling I am afraid that it does not go away, or at least it hasnt for me, but I make an effort to reming mey self that is its for the good of the breed,, mother and more importantly gives the remaining pinkies the best chance. It goes along way to making me feel better :|