Savage long action $325 dollars, recoil lug $35, Stockaded P-dog stock and hydro dipping $360, Brux fluted 338 med palma barrel $425, brake $120, EGW HD rail $89, Burris tac rings $90 and a Sightron SIII 6-24x50 $825. Total without labor and scope $1444 .
You can get a prefit barrel for a Savage in 338 RUM and put the barrel on yourself then do all the work yourself. The rifle is a 338 RUM and pushes a 300 OTM at 2800fps.
The other budget elk slayer build has the epoxy curing on the bedding as we speak but I've shot it a bit to verify potential.
Rem 7mag ADL with barrel and stock sold of $200, recoil lug $35, Hart stock $200, Brux fluted med palma barrel $425, brake $120, Nightforce rail $114 and rings $125, bottom metal $20 from a yard sale, pillars $39, Callahan . Total without labor and scope $1278.
The closest a guy could come to this without a lathe and stuff is to get a Rem prefit barrel with nut from Pac-nor and lap the lugs without truing the whole action.
It's hard to build a serious ELR elk rig on a super tight budget but it can be done especially if you gather parts cheap that guys are selling of and hit sales!