Mr. .45-70,
You were correct, upon researching your question I discovered that no 7600 carbines in 270 were ever made. The only 270 carbine Remington ever made was the 760.

Barrel length doesn't have much if anything at all to do with a gun being accurate or not! About the only way barrel length will help is by having a longer "sight radius" when using iron sights. If you're going to use a scope "sight radius" becomes irrelevant! Barrel length does help with increased velocity. The longer the barrel the higher the velocity will be to an extent. If the barrel is to long and the gases pushing the projectile down the barrel burn out completely, then the added barrel length "can but won't always" create friction and you don't want this to happen either.

You can always get the 7600 with the 22 inch barrel and have a "GOOD" gunsmith cut, recrown the barrel and remount the sight. It really an easy thing for a gunsmith to do!