What's the purpose of having one built "on the cheap"?
There are some pretty cost effective factory rifles available that make excellent long range shooters.
Factory rifles are the cheapest way to go. Remington Sendaro is another that can get the job done. You could get it in 300RUM and rebarrel to an Edge later on.
If you go full custom build, you will spend some bucks, no matter who does the work (if they are reputable anyway).
Even just buying a remington action is at least $400, a barrel is at least $300, stock, bedding, floor metal, scope base, trigger, action blueprint, gunsmiths time...??? At least 2.5, maybe 3 times the cost of a factory rifle when it's all said and done.
It's not polite nor beneficial IMO to ask a gunsmith to do sub-standard or cheap work. We generally get what we pay for, and the top tier smiths take alot of pride in what they do.