I'm starting to up my average, being sort of new to Trap (6 months). I started with a Modified choke, and 1200fps 71/2's - Now that I've improved my skill a bit, shooting 3 or 4 times a week will put it on fast, I'm working with Briley Spectrum Lite-Full and 1200-1290 1oz 71/2's. I found this combo to work for me from 16 to 27, I only change the load as I move back. 1200's seem to work great until I hit the 22yd line then I move up to 1290's and those work well from 23-27.
I've steadily worked on making my self more consistent, and honestly I think that helped up my scores more than Equipment, or Loads. I try and do the exact same thing every single time, in an effort to eliminate as much shooter variance as I can. This has brought my average up from 18-20, to 24-25 in a short time. Getting over looking at the end of the shotgun was the hardest thing, I'm a Pistol/Rifle shooter and moving from aiming to pointing was quite a culture shock for me.
Tons of good advice in this post, but, I think the best advice is to find your "ritual" and maintain it, Footing, Gun Mount, Hold point, and Call. Make it all the same every time and the scores will go up as you put more rounds down range.
NachO