Browells and Northland Shooters Supply used to carry them, but I can't find anybody who has them now. Your best bet would be to find a used rifle and salvage the action. Get an older one, since part of the reason that Remington is out of business is that for the last 10 years, they made certified junk. You would be lucky if the thing even worked, and the new triggers sucked. It's the kind of thing that happens when a bunch of corporate assholes watch a youtube video and decide they know more about making rifles than someone who has been doing it since the invention of steam engines. The actions came in long and short versions. You want a long action, with a standard bolt face (30-06, 270, etc.). You are still looking at well over $1500, by the time you get the doner rifle, have a barrel fitted, maybe a trigger, and then a stock. Your business, but my advice would be to find an original and finance it, if you have to. The resale on custom rifles is terrible. You would be lucky to recover a third of your investment, even if the finished product is better than the factory gun. While cheaper, you will have the same resale issue with a rechambered 22-250.
Your criteria is a problem. Remington 700 (out of production) and 220 Swift (custom chamber) don't mesh with "budget'. Budget options might be a Savage Axis, Mossberg Patriot, or Ruger American (Walmart stuff), but you won't find a 220 swift. A more affordable 220 swift option may be a Savage 110. Here you have an available action, non-gunsmith barrel installation, and the best factory trigger you'll find.