So, why the focus on 14.5" barrel? Why not use a long barrel (say, 18-22") but mate it with a bullpup receiver?
My M17S from bushmaster has a 21.5" barrel in a 30" weapon. It's MUCH shorter than my 16" barrel AR15.
The Kel-Tec RFB is a 7.62x51mm platform that is only 32" overall for a 24" barrel.
The
Desert Tech MDR platform seems built for what you need. It can be quick-converted from 7.62x51mm to 5.56x45mm with some part-swaps, the thing is only 26.2" long with a 16" barrel. Mounting a 20" barrel would make the thing a still-very-handy 30" long.
Anyway, if you want "1000yds" and "powerful" and "carbine" then you're looking at a bullpup.