Look at wildcat bullets. I believe there is a 140g ULD available. 1 in 9" would probly stablize the 140g. I dont know even know a rough BC estimate for that bullet. I only shot the 125g ULD as my 25-06 has a standard 1 in 10". I got around a .515 BC or so out of the 125g ULD @ 2950fps. Hope this is of some help.
Richard makes a 130 grain HP RBBT as well as a 142 gr HP RBBT. I do not know much about an AI but I had a couple of plain jane 25-06's. They should handle the 130 gr Wildcat pretty well up at the higher velocities. My limited testing of the 130 Wildcat shows it to be extremly accurate.
I used an online BC calculator on the 130 after measuring everything and it comes out to about 0.635 which is a pretty good BC for a 257 bullet. I have not tested the BC myself at long range. I will do that in the next two months.
Unless you have a faster twist then the standard 10", you'll be limited to the 125g ULD. I used it out of a Winchester model 70, in 25-06 @ 2950fps. Shot great out to 600 yards and hit really hard for .25 cal. I got a rough estimate of around .515 for a BC. Worked for me anyways...I used them to take a nice 4x4 whitetail that scored around 145" at 440 yards, and a couple coyotes from 100-600 yards. All bullets exited leaving quarter sized exits. Would have no doubt they would be superb on goats as well.