My apologies to the OP as I just noticed at the bottom of your original post you were going to use an Axial Precision Action and CF stock......ill leave my post up anyway
If your on a budget best route for an Ultra Lightweight Sheep hunting rifle is to grab an used Kimber Montana 84M, they have an excellent adjustable trigger, a lightweight kevlar-CF stock which is easy to modify, and a very lightweight CRF action,
Adjust trigger to 2.5lbs,True&Square action,rebarrel it with a Benchmark #1 contour SS 20"-22" barrel, 6.5CM, 7mm-08,6.5-284 any of those calibers are fine for sheep, Gunkote in your fav colour and paint stock, add Talleys and a VX3i 3.5-10x40 CDS, poof your good to go at a reasonable cost.
Heres a Cpl picture of Kimber's we did just that to.
This is my son Brad's Kimber Montana 7mm-08 with a Benchmark #1 SS Barrel 22",Pewter Gunkote,and stock painted green with fine black splatter, Talleys and a Swarovski 4-12x50 BT Plex
Next up is a Kimber Montana 84M action, I had built and donated to the WSS of BC last year, trued squared and slabbed action, Benchmark #1 SS 20" barrel chambered in 7mm-08, cheekpiece added to the stock, it weighed 6lbs scoped, this rifle shot one hole groups with Nosler Trophy Grade 140gr ABs.
here's my factory stock Kimber Montana 6.5CM with a facelift, it shoots well enough I haven't had to rebarrel it yet, High comb and cheekpiece on the stock, gunkote and painted.