I'm not sure I understand your question. You say you can't afford a custom, but building one from scratch IS custom...and accurizing a Rem700 requires smithing, so your cost savings will be minimal. Accurizing a Rem700 factory action costs nearly the same as many of the custom 700-footprint actions.
The savings you have will be using the factory barrel, and that's the first thing I recommend you replace. My current long range 300WM IS a factory Sendero, and the barrel -- while very accurate -- must be soaked in copper solvent every 12-15 shots to maintain accuracy.
If you want a good-shooting rifle on a budget, buy a low-end Savage and build it yourself. Several makers will sell you a chambered, pre-fit barrel in the $350 range -- and will throat it to your dummy cartridge. Then you install yourself for $0 in smith labor. A decent laminate stock can be had for $160, and composite in the $200-$300 range. Install pillars (if lacking) yourself, do the bedding job yourself.
Now you have a custom rifle ready to shoot for only $550-$850 more than the cheap basic starter gun...pretty close to the price of a high-end factory rifle.
I'm doing this with a 243AI right now.
I had a rifle built by a well-known smith last year. It's an excellent gun and the particular work I needed I could not do myself. But accuracy-wise, I've had no problems getting what I wanted assembling myself on a Savage platform.
I agree all though I am not even close to the 1000 yard range. I took an older savage 110 action my brother had, bought a match grade prefit criterion barrel varmint contour for 350 dollars. I was fortunate I could get the older stock trigger down to 2lbs 8 ounces so I did not need an after market trigger, if you got a savage with an accutrigger then you would not need an after market trigger. I bought a Bell and Carlson stock for 250 dollars. Bought the action wrench and gauges needed for barrel swap. Though it is recommended to further bed stocks that come with aluminum bedding blocks, I did not. I have tested this rifle to 400 yards and it is still maintaining .5MOA if I do my part. These are 3-5 shot groups. The chrono numbers are solid so I do believe it could be a shooter past 700 yards but I just don't have the range to do it.
As for cost:
Used savage rifle or newer savage action: 300-400$ dollars
Barrel: 300-400 dollars depending on what you want...if brake is needed call it 500$
Action wrench: 65$
go/no-go gauges:50$
New barrel nut:25$ (not needed but you might want one)
New recoil lug from SSS or NSS: 30$ (I would definitely buy this)
Stock: 100-700$. You can get a nice boyds laminate for 100 but you WILL have to pillar bed it. Bell and Carlsons go for 250-350 depending on model. HS-precision is 350, manners and mcmillans will be 500+. The type of savage action will limit which stocks you can buy. Choate stocks are typically heaviest and one of the cheapest and sometimes need work to fit well but will do a good job afterwards.
If you go the cheapest routes possible you are looking at 1000$ with the tools needed to change the barrel yourself. You could either sell the tools afterwards to re-coupe some of that money or keep it for possible future builds. If you buy a used savage rifle that is in decent shape, you can typically get 40 bucks for the old stock and 60+ for the barrel you take off. Sometimes upwards of 150 dollars if it is a desirable caliber.
If you go more expensive and get an HS-precision stock or manners/McMillan, you are looking at 1200-1600. The manners and McMillan stocks will have to be pillar bedded as well. If you cant bed a stock yourself this costs typically 200 dollars by a gunsmith.
All these builds will outshoot any factory rifle and will most likely get you to 1000 yards but as you can see at the upper range of these builds you are starting to approach the cost of a "USED" custom sold in the classifieds here. Personally I like to tinker so the savage builds are cool. Once you buy the action/stock you can basically have any caliber you want with little or no effort by changing the barrels out yourself. If that was your desire I would buy a savage "long" action. YES, you can use a long action savage to build a short action cartridge. Some people do this intentionally so they have longer magazines which allows them to load bullets into the lands especially when using burger bullets.
My rifle is currently a 7mm rem mag. If I ever got bored with that cartridge, I could buy a new bolt face for 25 or so bucks, a new match grade barrel 300 bucks, set of go gauges 30-50 depending if you want the "no go", sell my old match grade barrel for say 200+ dollars and bamn I have a new cartridge built on an action and stock I know already works for me for little extra money. this is of course as long as the new barrel is a similar contour to the old.