The Savage Axis is a budget/entry level hunting rifle and, in that role, is a good value for money proposition. As a target rifle, particularly at the ranges you propose, it will never be suitable no matter what caliber it is chambered in. It's light, notoriously poorly bedded, has a relatively flexy stock, and its recoil "lug" is not ideally suited. For 800 yard work, you will need to spend @ 4-5 times the cost of the rifle in glass.
This idea is a waste of your time and money. You can get a used Savage 110 action target rig and decent glass for under a grand with patience. A Savage Axis is an entry level deer rifle.
For example:
https://www.thehighroad.org/index.php?threads/savage-axis-poor-accuracy.873173/#post-11601791
I agree with that in a lot of ways.
From my experience the STOCK AXIS tend to be very mechanically accurate, with little or no difference between the heavies (only shot one of those, so take it for what its worth), and the lights. BUT the stock rifles tend to be difficult to shoot consistently as compared to many others.
https://rifleshooter.com/2016/05/customizing-the-savage-axis-easy-upgrades-that-enhance-performance/ list the upgrades (tho id have got with a more traditional Boyds ProV stock, and saved 200 bucks) ID want as a minimum on an Axis rifle i was going to keep.
That dosent mean that someone CANT take an Axis to 1k or more, In fact its probably quite common for at least some Axis rifles to be shoot at that distance. If the gun and shooter are capable of producing consistent 1moa or less groups at 100yds, then they should technically be able to produce similar results at any range beyond that (as long as their ability to read, and compensate for environmentals is good enough).
Where I think the stock Axis, and my beloved Americans for that matter, struggle is making it easy to deliver consistent performance, at least for less seasoned shooters.
Case in point.
(Im not saying Im a great, or even good shot, in relating this story, but im pretty consistent within my limitations, and regularly deal with less than spectacular rifles)
I helped a friend sight his Axis .223 at the range last saturday. Box stock, used, and still had the cheap package scope it came with.
I sighted it, shot a decent group and turned it over to my buddy who ISNT a rifle nut (yet). His groups were well over double what I got, so we swapped back, and the gun turned in another decent group.
He spent some time shooting my Ruger American (in a boyds stock with trigger work, decent scope, and significantly more weight), and produced much, much better groups. I attribute that mostly to the fact that the Rugers a lot easier to shoot than the Axis, as its not any more mechanically accurate (from what i could tell after firing 12 or 13 shots)
I also dont think the Axis is a great platform to START a build specifically for long range shooting, mostly because for the cost of all the upgrades it would take to make them as user friendly as id like. You might as well buy a higher end rifle.
that dosent mean someone who WANTS to use an Axis for such, shouldnt do it (Heck, ive done way less practical/sensible stuff just to say i did it), or wont be able to achieve what they want. Just that you need to realize WHY your doing it. It also helps if your willing to do a bunch of tinkering with the stock components.
Also to be fair, there are very few budget-middling factory guns Im 100% comfortable with. I really like Ruger Americans, but every one ive had, has at least gotten a stock change. I like Savage 110/10s but they also usually get modifications. ALL rifles get bedded and floated. The only gun I own that hasnt had anything major (beyond bedding and a new bolt knob) is my Ridgeline.
