Phil, lots to think about with what you are wanting to do, and everyone on this forum is going to have a different opinion and way to get to the right place in the end. So here is a little more information for you to chew on.
First thing and I believe this to be very important is forget about the Savage all together on a Point Blank rifle, you did say 100 to 200 yds. They while very good rifles in some sports are just not suited at all for Point Blank Bench Rifle. The precision needed for this very technical sport is not going to be found on many if any Factory actions. The 40X may be the exception, but even it may very well need some work. To verify this look at the equipment lists for a few Benchrest Matchs, they do post a list. There you will see what is winning and what isn't and you will find ( I believe) at least 99.5% or more straight custom actions.
If you do decide to go ahead and do this yourself from the beginning the big negative is going to be the time it takes to get all of the parts you will need to put this together. That could take realistically 1 or 2 years, and then you will need to find a Smith and fit into his schedule. Also the cost is not going to be cheap or even reasonable not by a long shot. I have done this both ways and it is not hard to spend $5,000 to $8,000 on a rifle depending on the components you end up using. I am not saying it can't be done on a budget and for less money than that but things can get out of control real fast.
I believe the best way and certainly the fastest way is to purchase a rifle on the used market. Take your time and be sure the rifle is one you really like and want, has a good stock, custom action, trigger and all of the other stuff, and you "CAN" buy one of these in the $1,200 to $3,000 dollar range. This way you get a rifle in this life time and you can be out shooting it in a week.
As I said I have done this both ways, built from the ground up, and purchased used ready to go. I have these rifles today and would not part with any of them.
A couple of pit falls you may have to address. Stocks are one of those, the rules on stocks in the short range games is pretty well set in concrete, be sure the stock you get is one you like, and one that is legal. Usually this is not a problem as most of the used Rifles are competing now. The other thing is barrel count, some rifles just may have high barrel count on them, many, many used rifles will come with more than one barrel by the way. If you do indeed have to make a barrel change, and I personally would count on doing that first thing, there are a lot of new Kreigers, Bartlein and other barrels available with no wait from vendors right here on this site. Just this past week I ordered two Bartlein, and two Kreigers from Grizzley and Bruno's. The Kreigers I had in four days and the Barleins only took two days to get to me.
Benchrest Central in there classified has right now about 15 or so competition bench rest rifles for sale. Prices run from $1,400 to $2,800 for a Stiller drop port with only 260 rounds on the barrel.