A Savage makes it easier, but you'll still need to take your barrel to a machine shop and have them "face" the breech end of the barrel. Hopefully you already have a Savage barrel nut wrench - you'll need one.
Pull your barrel off
Drop a FL resized piece of brass or a Go Gauge down the chamber
Measure how much protrudes
Go to a machine shop and have them take .060" off the breech
Rent/buy the AI reamer and reamer "T" handle
Rent Go/No Go gauges (you might be able to avoid this if you keep your FL sized piece of brass segregated/marked and are feeling lucky).
With LOTS of dark/high sulfur oil, flush the chamber with oil as you hand turn the reamer
Stop and check often - using the Go gauge or your FL sized brass - for the same amount of protrusion you had before you started.
The lucky part comes in that your sizing die has the same headspace spec as the reamer. Even though you are going to an Ackley, it still should headspace on the brass OK. I THINK the No Go standard chamber gauge is used for an Ackley Go gauge. I could be wrong on that, I have to look it up every time too.
IF you go too deep with the reamer, your headspace will be excessive. If you know how much excess it is you can go back to the machine shop and have them take off the additional length to get your protrusion back to where it should be.
If you want the Savage barrel lettering to line up where it is now, tell me if you have a small shank or large shank Savage. I'll look up the thread pitch and tell you exactly how much to take off the breech. The 060" was just a round #, but if your barrel has lettering and you want the lettering in the same spot, you'll need a more precise number.
FYI - I am not a machinist or gunsmith. I am a truck driver that dabbles with a lathe in the wee hours of the night.
When the machine shops dials in your barrel to face it, if you are standing there with the reamer and gauge(s), it would be real easy to ream the chamber then - to the correct depth. I would think that in MI, there are a lot of out of work machinists or small machine shops that are slow and will do a cash job while you wait (watch).