I have a Model 70 375 H&H here - serial number on receiver has a "G" prefix (in a different font), and it does have the "anti-bind" lip, so I think it is 1968 - a push feed, of course. Pretty much standard - Winchester hinged floor plate, etc. I just tried it - accepts 3 rounds into magazine, then will chamber a 4th round inserted into chamber directly - can not put fourth round into magazine. Same as my push-feed Model 70 in 338 Win Mag. So, the rifle shown above has standard capacity mag - if not from Winchester, then similar size. Extra depth on the stock would be required for the "wood bottom" as shown on the OP's latest picture.
As for the comment about one piece base and mis-aligned scope base holes - if such is really an issue, then Redfield, Buehler, Millett, Leupold and others make two piece "twist in" type front bases with windage screws on rear base that accomplish the same thing.