There may be a further problem with getting a barrel with the correct spin for an air gun. I am GUESSING the spin needs to be faster than for a .22 short. And,a .22 short spins faster than a long rifle. I can't recall the spin offhand,but if it isn't right,accuracy will be miserable.
I used to have an old "Apache" air rifle from the 50's that had a .25 caliber barrel on it.It belonged to a friend of mine who is several years older than I am(74). I don't know if I still have the gun or not. It did not work since the seals on the piston long ago gave up the ghost. I'll look around and see if it is here.
It's barrel looked more like a barrel liner looks than like a thicker normal barrel. It was an old pump up design. A friend of his told me that the old gun shot "like the hammers of Hades" when it was in use.
Anyhow,getting a .25 caliber projectile to nearly exceed the sound barrier is not going to be the easiest thing to do. I have a big,heavy duty "Kodiak" sir rifle in .22 caliber that does 800 FPS. It would do a lot more in .117 cal..
How are you going to propel the projectile?
Aren't there some kind of super air rifles made in the Phillipines that are large caliber? I have seen pictures and read about them. Rather gaudy looking,but powerful. I can't recall particulars.