Remember that the point of SAAMI specifications is so that any SAAMI chamber will accept any brand of SAAMI-compliant cartridge. This is very important if you are building a rifle for someone else, who may off in the wilds of somewhere & have to dash into the nearest sporting goods store & buy cartridges.
Now consider the difference if you are building the rifle for yourself, for competition. As soon as you go to tight necks -- or at least, those tight enough that a turning tool will have to be used -- you're no longer "SAAMI."
Not recommending anything in print, but one could buy their brass first, and check the length from the casehead to the neck/shoulder junction and to the body/shoulder junction.
(Or use the reamer to make what alinwa calls a "gizzie" -- a short section of a scrap piece of barrel with the reamer run in just far enough to cut the neck, shoulder and a tiny bit of the body. Ends -- or at least the end above the neck, which you will use in measuring operations -- cut true in the same setup as you cut the chamber portion.)
Whatever your measuring device, make the same measurement on the go-gauge. Remember, the number you are after is a difference, not an exact length. You also know the TPI of the tenon thread, so know how much clocking the barrel will change chamber depth.
All this is just information. If you believe, like some, that brass matters a lot, and the best brass comes from fireforming in a chamber where the virgin case is a crush fit, there are several ways of doing that. One is to alter the brass (before fireforming) to fit the chamber. Another to alter the chamber to fit the brass.
Or, as Boyd pointed out in another thread, you can set everything up to fit an already-purchased, off-the-shelf-die. That would require having the die before the reamer is ground, because there are diameters at play, not just length.
You get the idea. Fitting things closely can be done in a variety of ways. SAMMI is a standard everybody agrees to in advance, so brass, camber, and dies all allow variance. The SAAMI system comes with necessary compromises, ones needed for interchange in a commercial world. If, for you own work, you pick one of thing (brass, chamber, dies) as a standard up front, you only have two other things to make compliant, and less compromise in the whole system.
These are things you can only do in your own competition rifles, not work for the public.
Finally, remember that as you tighten the nut on a Savage setup, the action will try to rotate as well. The barrel is held in a vice, but not the action. It will try to rotate a bit. Check with your gauge again after tight.
I use a "Savage nut system" on my 1K Heavy Gun. The back end of the nut sets the cartridge head clearance, the front side of the nut is machined as a cone, to center the whole barreled action in a large diameter tensioning tube. Nothing wrong with a "Savage nut" -- just different advantages and compromises.