This is an easy fix , 6x47 Lapua and here is why
1) very close to the same case size as your 22-250
2) will out run the 243 Ackley in the same length barrel,close to the 6x284
3) not overly hard on barrels , 2000+ rounds of competitive barrel life !!
4) Lapua brass in 6.5x47 , so all you have to do is run it in your FL die and
5) its inherintly accurate at very long range.
Use a barrel with a 1-7.5 twist , you can shoot bullet fromt he 55gr ballistic tips to the 115 Bergers , though you may blow the light weight bullets up trying to run them above 4000 fps. but a 75gr V-max would let you take coyotes out to 700-800yds , but the pelt may be ruined.
here is a link about this round i posted some time back about it being a good varmint round , i had built one on a M-7 remington and sold it to a fella , his E-mail to me about it is under the pics
Long range varmint caliber , 6x47 Lapua !!