Start with 90 gr of H-1000 and work toward 92 gr in 1/2 gr steps under a 300 gr SMK or a 300 Berger OTM. The Bergers will group quite a bit better at 1000 plus. Use a CCI 250 primer. Start with them seated .020" off the lands and see what ya get. I would not recommend using a solid copper in that new tube until it is well broken in. Well,,,,, I would not recommend a solid anyway..
But thats just my preferance after seeing 10 or more elk go down each year.
The 5.5~22 NXS is hard to beat in my opinion. It serves me well on my 338 LM to well past 2000 yards.
Good luck with the new stick.