You could, in theory, find a rimfire frame that matches the tolerances on a centerfire frame, get a 17 cal barrel fitted to the rimfire, and rechamber it for 17 Rem with a .223 ejector. I'm not sure what the point of a 22" barrel with all that powder behind a 17cal bullet would be. I'd love a .17 k-hornet myself, but Lee doesn't make dies for it, and RCBS dies cost more than the barrel. I'd just use .22 Mag or 17HMR for close shots, or get a .22 hornet or .223 for longer shots.
The 24" .223 is nice to shoot, but the barrel alone weighs 4lb, 10oz. With the scope MSP mentioned, factory scope caps, aluminum Weaver rings, and the lightest stocks (low comb synthetic), my 24" .223 weighs 8lb 13oz. Since you'll never overheat any barrel shooting yotes, it's likely not worth dragging all that weight around. If you buy the H&R ultra with laminated monte carlo stock, it will weigh a fair bit more than my synthetic.