I'm a little late for this party but here is what I can recommend. I grew up using this cartridge and been using it for over 30 years.
You need a fast burn rate powder like IMR-4064, IMR-4895 or Varget, monolithic bullets are longer and will reduce you powder capacity so powders like IMR-4350 and others might not give you the velocity you need. In some rifles you can't seat bullets out more than the standard COAL of 2.80" so this limits powder capacity as well.
Now some monolithic bullets like barnes need a high velocity impact to ensure expansion so the 120gr might be your best option. You might be able to push it at around 3,000 fps in this cartridge with your 22" barrel. The heavier ones might just pencil through and produce a slow kill or even worse loose a wounded animal. I've seen it happen but luckily we recovered my buddy's deer a mile and hours later, with a broken front shoulder but hardly any damage to lungs.
My wife uses 42.5gr of IMR-4064 with the 120gr Ballistic tip and we use 24" barrels on ours, she gets just over 3,000 fps with this load.
Hope this helps.