How about the .22 Bench Rest?
Actually, I'm not a fan of the .22-250, although I really like the "Swift." I hunted with the Swift one deer season and did quite well with it.
But the .22 BR ..... Just that I've always had a hankering to try the .22 BR (to be different) and scratch that itch.
Of course if the Handi barrel was only 22inches I might decide to do a rebore to a 6X45 or 6X47, or even one of the TCU rounds (.257 or .264).
Edit: Before I did a .225 Winnie, I'd stick with the Swooft - as it is much more popular to find brass and probably offers a slightly bigger case capacity. The .22 BR offers similar performance to the Swooft (and is every bit as good as the .22-250).