I have a 60's L579 which is very different from yours so my suggestions are more generic or from my WSM experience.
Regarding the recoil lug:
If it were me, I'd bed the recoil lug to the stock. Then again to the action. Making sure to load the action forward so that the rear tang was relieved of pressure as much as possible.
Regarding 300WSM for the original caliber. I have this chambering in a Weatherby Vangard. Stock barrel load development for 6 months never achieved what I want. Since I was not satisfied with the original barrel I changed it to a Pac-Nor. Now shoots so well I feel confident in competitions and of course hunting. Factory copper is sub moa.
Since you are considering rebarreling, if it were me I'd go 6.5-300 WSM or 7-300 WSM 8 twist for both. 6-300 WSM for me would be too overbore but would be quite a chambering again go 8 twist as you will probably shoot long bullets. To make the dies for 6, 6.5 or 7 WSM, get a reading S die for 270WSM or 300WSM and bushing set for your chosen caliber. All other dimensions are the same.
The most important thing if you change, do what you would enjoy.