Your rifle originally would not have had a laminate stock. So the one you had shown would not be period correct.
Secondly, regarding your question: the trouble I see is the same as others had pointed out - the welding was good, but blueing would not help as it is now. You will always be able to see the round holes. The welder has to do better, and then file it carefully flat until it fully matches the receiver contour. Secondly, why I also concur that reblueing is a bad idea: a friend of mine did high end restorations for a museum. Therefore he mixed the original receipt of blueing solvent he pulled from WWI instructions and had the Chemistry University mix it for him (what btw was a tough job for them too, since many components are no longer easy to get). He then applies it as officially instructed/done at factory (what, mentioned in this context is what we'd call "cold blue" as well; just to have it mentioned). What was most interesting to me (and also the reason why I mention this here), he said when something is welded and then blueing should be applied the steel used for welding needs to be of similar material as the rifle itself. Modern welding wire otherwise will result in completely different colors when being blued. His personal experience was that at least for WWI Austrian guns the wire used to bind bouquets would result in identical blueing color.
So even if you let your rifle be hot blued/dip blued by a professional you are very likely to notice miscolorations on where it was welded, simply if not a material of same steel components as the action was used. Therefore I tend to agree with others in here: if you cannot assure the material is identical, then just have the welding done in that it is excessive material all above the hole, and then extremely carefully hand file and polish it back to contour. Since the area around the holes has very little blueing left, then just try various cold blue mixtures and afterwards just polish them off enough to partially match the rest of the (visible) action. If you will blue the whole action you'll make them better visible than you could match with what I had mentioned.