It sounds like you have a wonderful rifle in your possession.
I would recommend the 215 Berger hybrid target bullet. I has a fantastic track record which I will link at bottom.
My friend asked me to make him a LR load for his Browning A-bolt in 300 WSM with the BOSS system. The barrel is 22" perhaps 21" long, hard to tell with that contraption on it. This is where this gets crazy and the facts will make a point. I had some 230 Berger hybrid targets on hand and gave them a try. To get the loaded round to fit and feed from the mag box I had to use an overall length of 2.8". I thought it would reduce performance considerably seeing so much of the bullet inside the case. It worked out well. It was accurate and it obtained respectable velocity. Using Fed 215 primers and working up to 61 gr of RL-17 for an amazing 2735 fps!
If this rifle can do that with such a long heavy bullet I am positive your rifle will work well with the 215 gr version of this bullet. In addition the hybrids have proven to be seating depth friendly. Many of the rifles I have loaded with hybrids never required any seating depth changes. Just work up a powder charge to find best accuracy.
Now for the 215's hunting abilities. A fellow LRH poster, Broz, did what I consider the best
documented hunting performance thread on any bullet I have even read. He used a 300 win mag for all the kills. I will skip the beginning which discusses the 215 hybrid vs the 210 VLD. The velocities and energy values are listed as well as entrance, interior and exit wounds. The velocity of the bullet at each distance will help any reader determine how slower cartridges will perform. IIRC there are 23 one shot kills here:
http://www.longrangehunting.com/forums/f19/comparing-berger-210-vld-215-hybrid-88657/index12.html
I hope you find this information helpful.
here is pic of 230 in the 300 WSM