I re barreled my 270 wsm to 7 saum. I'm very happy with the result.
However there seems to be a shortage of saum brass right now. Things may improve later.
I think if I was to choose any of the short mags now
I would choose 300 wsm. ( In fact I did. ) Lots of brass. shoots a wide range of bullet weights and styles. The barrel will last a long time--2000 or so. As accurate as any thing.
You are going to be limited to any of the SAUM, or WSM configurations. You can not go to a 300 win mag, due to case length. The LA 300 RUM, definitely not.
The 300 WSM is a great option, as is any of the WSM bullets. I had one of those, in the rifle that you have, and it was incredibly accurate. I know what you mean about the brass.