A carbine might work for you. I find a heavier rifle is easier to shoot far and accurate with. My National Match is around 13 lbs. I have lead in the handguard and the buttstock.
The sight radius on the 20 is more conducive to aid the shooter in accuracy.
The 16" and 20" are both capable of shooting 3/4 MOA. The big difference is velocity. The 16" will need more hold-over than a 20". If you can do the 15-minute trigger job that can help too. Polish up engagement surfaces and smooth things out. If you have a nice trigger long-range accuracy is a lot easier IMO.
It can't hurt to try things with the carbine. I think from the last one that was held there were some people that never did hit the target even with the right equipment.
I'd also be using 69 or 77 grain BTHPs, especially in the early springtime in the valley.