My wife uses a lightweight 270 Mountain Rifle for elk. She is a fairly small woman but has good form so the recoil does not bother her. She uses a bit of extra padding when she shoots from a benchrest but recoil from field positions is hardly noticeable. She has taken elk cleanly with her little 270.
As you have very recently taken up handloading you can put together cartridges for her rifle for practice that will have reduced recoil. Just sight the rifle in with full power loads before season for shooting at game.