.223 and 5.56 will both work in the DDs.
The geisselle trigger is a custom trigger with a pull weight around 2.5-4lbs. Crisp and clean breaking trigger. Milspec is just the stock factory trigger that comes with any off the shelf AR. The Geisselle will cost you money! Is it worth it? That depends on you, how much you plan on shooting and competing. I use milspec triggers in both my ARs and I have no problems.
Check out TAC Rifle at Thompson Mtn. Go to the Tacmatch.com site to sign up for details.
Another venue is Chilliwack Fish and Game. Their black rifle section has a parallel and close relationship with TMSA and will see more events in 2016.
PS If you really want to compete with your AR and will only get one AR, get a 16" model. This gives you flexibilty if you ever want to shoot in the States as that is their min barrel length requirement. Also, they will not admit Norinco or DA rifles.