I wouldn't worry too much about the strength of the stock as from the looks of it, it has been restocked and the grain layout through the grip looks just fine.
I have shot four of my vintage 303s with factory 174gr ammo (2 Gibbs Farqs, Jeffery Farq, and a Lee Speed) with no ill effects other than a dragging firing pin on the small Gibbs. Accuracy varied but the Speed is quite accurate with everything I have sent down the barrel.
They all fire formed to their respective chamber dimensions and the Jeffery and older Gibbs are definitely a little different than the other two. Unless you plan on keeping specific brass for your Jeffery, you will want to figure on full length resizing.
All modern 303 loads have the .311" bullet afaik so there is no worry about bullet diameter really.
