To “neck down” a cartridge you will need special custom sizing dies. To go from a .50 to a .223 you would need several sizing dies each one a little smaller then the other, since going from .50 to .223 is to large a step. By the way the .223 bullet is .224 not .223. Another thing, there is a point of diminishing returns when it comes to wildcatting, a cartridge can only be necked down by so much and a bullet can only be driven so fast, before things start getting really messed up. Like over a certain velocity a bullet will disintegrate upon leaving the muzzle, and worse yet if you neck down a large cartridge case too much it may increase the pressure to a dangerous level.
Wildcatting is a hobby in and of itself and you really should have some special equipment like a strain gauge to measure chamber pressure and a chronograph, plus the special sizing dies you will need will have to be custom made the same as the chamber reamer that will be needed to make the barrel. So unless you really want to get into a new hobby and are willing to spend the time and money that will be needed I would suggest you just find another cartridge that has already been fully tested and works, either a factory round or even one of the wildcats that has already been developed by another wildcatted. If you are still interested in trying this then I wish you the best of luck and please get some professional advice on how to do this safely.
I am not familiar with the 50AE round but I think you will find that trying to use a 50BMG case to fire a .224 bullet will not work out, even if you could find the sabots the pressure would probably be too high and you would be trying to push the bullet way to fast.
And last if you want a very fast .224 pistol just get one of the single shots that are chambered for the .223 Rem or the 22-250. The 22-250 and the 220 Swift are the two fastest 22s that are available. And for your 50BMG project just get a 22-250 or one of the custom rifles like a lazeroni they produce some very high velocities.
Sniper for Justice
VINCE AUT MORIRE (Conquer or Die)