Which One
If you want to stick with a 22, go with the 22 BR, keep the same twist rate as your current 22-250, it might not handle as heavy as a bullet as the 22-250, (it does, after all, use less powder), but it will eat 60 grn pills with no problem. The 22BR is known for it's top notch accuracy potential. And yes, it will handle 500 yards with no problem.
You can get a little better accuracy at 100-200 if you opt for a slower twist, in the 1-14 range, but you will be limited on the weight, and length of bullet you use for longer ranges.
If you are not totally in love with the 22, build a 6BR with a 1-8 twist. It will do the job out to 600 yards, with great accuracy at anything in between........jackie