1st, there is nothing cheap in the NFA world unless you own a machine shop. It's just lighting $100 bills for fun.
2nd, while you could thread your pencil barrel for $130ish, it is a pencil barrel in the end and POI is most likely to change from off to on as you hang 12-16oz of material on the end of that twig. Also, the mirage is going to be a PITA after round 3 on that light of a barrel. If it is one shot hunting, you'll be ok with the mirage.
3rd, Savages are easy to change with their nut system, but you need, a barrel vise or some vice with padding, the barrel with nut ($500ish), the nut wrench to match the style of your barrel nut ($20-30), and go/no go gauges ($60-80) for your caliber. With all those items, its less than an hour of work.
I'm a rem guy but I've built 2 guns using the remage system which is the savage nut style on a Remington thread taper. They were heavier tapers and no POI with my Omega can.
If you want the least POI change for the cheapest, sell that and buy one with a thicker barrel, 110 Savage, Bagara, used rem 700 SPS.