It goes against my better judgment to get into this, but since I have swapped barrels and headspaced many, many Savage barrels over the years, (most of them in a prairie dog town) I think I can add a little something to the discussion. I will add that I have never used or even owned a headspace gauge for one of these barrels and I have never had a problem, ruined brass, blew a case etc. Most of the time we tend to overthink this stuff. I would suggest that you not use the 5 times fired case, but rather use new brass. You really can't get any better than Lapua, so if that's what you have on hand, use it. Place the new case in the bolt head, close the bolt and screw the barrel onto the action/case. You want a snug, slightly crush fit. It's a good idea to keep the lugs well greased. I almost always need to adjust the fit several times to get the barrel nut to just the right feel. There's no need to rush it, just keep working at it until you get a smooth bolt close with just a bit of firm pressure. Then you might try another new case to assure that the feel is the same. An Ackley chamber should accept a new factory round and that's just what you've made.
Rick