I also just finished a Stag lower (my first AR build), and noticed the same two problems. You can cut the wedge shorter a little at a time, if the upper is loose. I did not end up using the wedge. Maybe later.
Second, the Stag trigger has lots of engagement on the trigger, sear, and disconnect, and a very long take-up. Probably for safety/liability reasons. I stoned the contact surfaces - don't take off any metal - just polish. It helps a lot. It is still long, but much nicer.
Conclusion - if you want a target rifle, Spend $100-$200 and get a good target trigger. If you want plinker or self-defense rifle, work with the stock Stag trigger, a stone, and time. I know more about pistols and bolt actions, but I think "engagement" is your friend for anything except target shooting. In both rifles and pistols.