I couldn't find a budget stainless Remington or Tikka action in stock in my brief search, but if you could find a long action or used rifle for less than $500 something like this could be an option for you:
Remington 700 SPS Stainless: $850
Sell barrel, trigger, and stock: -$150
McGowen shouldered 1:12 22" barrel: $375
McGowen barrel install: $220
Timney Elite Hunter: $170
McMillian Game Warden 2.0: $750
TOTAL: $2,215
If I were starting from scratch with a $2,000 budget, I might try something like this:
Savage 110 storm: $800
Sell barrel, trigger, and stock: -$250
McGowen 18" 1:12 w/ ⅝ threads: $370
Machined recoil lug: $35
Barrel wrench: $30
Go gauge: $35
Elf trigger: $170
XLR Element w/ folding adapter and mag: $620
Taccom Cheek Riser Adjustable Buttstock: $170
Magpul K2 grip: $20
TOTAL: $2,000
…except if I was starting over on a fast-twist 35 Whelen build, I'd probably go with a fast twist 338-06 AI for higher BCs and bullet selection (sorry for going completely off topic here).