The 17/22-250 has been done already. Called the "Flintstone Super Eyebunger" you can find the info on it in P. O. Ackley's Handbook for Shooters and Reloaders, Volume 2.
Short bit of information given says it's way overbore, obviously, and that the 25 grain bullet would penetrate 1/2" inch of mild steel at 4500 FPS. Tests were done with a 24" Barrel and loads listed top out at 4444 FPS. Some of which, it's stated, would be too hot for other rifles.
Same volume gives velocity readings up to 4187 FPS using the same bullet and the 17/223 Remington Magnum case.
Hard to come up with something new on a case thats been out for more than about 24 hours it seems.
Mike