I look at your whole project like this. Even if you do it over 100%, the best you will have is a nice rifle that ultimately has more value to you than it would have to most others. And probably, sounds like, it's not going to have any increase of value past what you put in it. Most likely less. So, with that in mind, and the fact that you have lots of guns to plink with if that mood ever strikes, I would think that doing something that looks nice, keeps some original parts, and gives you something that someone ELSE might look at and appreciate, will mean more to you than it means to yourself. That said, I just can't see an H/S stock in the mix. I'm assuming you are talking about the synthetic ones. If they made nice looking ones, then I retract that statement. But, I've never seen a nice looking one. I've owned em, like the function, just never really enjoyed them aesthetically.
Now I know you're not a whole lot like me! hehe. But, I've shot a BR rifle or two in my day, and I know if I was in your shoes, building a gun like this, I'd be kidding myself if I thought for a minute it would get any trigger time. I have rather nice BR rifles that were thrown in a closet and will never see the light of day again. I can appreciate it having sentimental value to you, and I can even understand wanting to do what you can to make it shoot well. At the end, it'll probably shoot 1 agg, and it will be put away to be appreciated in other ways than at a bench.
Do you even hunt? I personally do not any more. If I shoot something, it is for varmint cleanup around the buildings. Anything not causing damage to a structure or garden around here is welcome to live and let live. They're even welcome to eat the corn and knock it down if they want.
The checkering, I'm not positive, but I'd bet even money it was original.