Mike, the axis rifles are reasonably priced guns. Have you considered just selling yours and buying a 243? I realize a trade would be a good thing but you could be shooting a 243 by next weekend if everything fell in place.
Or you could get into reloading and make some reduced pressure rounds for that .308.
I had my wife shoot the .308 which I have, it's a savage with thick barrel .
She did not like it.
I got her a .243.. she said it kicks about like the .308.. yea the .243 was lighter.
I felt it didn't kick as hard as the .308 but her perception was it was still too much.
She does not mind full house loads in 357 Mag from a 6" revolver and I have guy friends that do not like those.
I built her an AR in .556 from Palmetto and she loves it, you can't get it away from her unless she is out of ammo.