IN my brother's Rem 700 long range, R#22 with a CCI 250 primer is doing 3000 with the 165 GS, load is at the top end of pressure in std Win cases. Groups at 500 he said were unbelievably small. My brother is a precision reloader and knows how to tune a rifle, loading at the range. He has bedded the rifle, floated the mag box, free-floated the barrel, and has a muzzle break on the barrel.
H and IMR are the gold standard for 165-180g bullets in the '06, approx. 57g
My Brother's choice of R#22 offers another great option. We have to work with what powders we have. I shot 165g Sierras with 49g of IMR 4064 into very small groups with standard sporters, and the BTHP of this Sierra is a very tough bullet.
I would start by seating the Sierra's .005 off the lands, if you do not achieve immediate success, then start at .020 off the lands, you should hit a payday.
R#26 with a cci 250 should achieve some eye-popping velocity with accuracy in the '06, and I would opt for Lapua brass if possible.