I built a 6X45 AR with a Black Hole Weaponry barrel a few years ago. With the now-discontinued Sierra 80 grain Single Shot Pistol bullets (I lucked into 500 of them), I am getting right around 2700 fps and superb accuracy (20" barrel). It has accounted for three whitetails and a few coyotes.
I picked up a Remington .223 for basically nothing a while back and considered doing exactly what you are are planning, OP, but I decided on building a 7TCU instead. I made that decision so that I could shoot the excellent Nosler 120 grain BTs. With a 20" barrel, I should be able to get close to 2600 fps. I did have to modify the mag box to fit the longer cartridge and I may have to do a bit of feel lip modification due to the "blown-out" body taper on the TCU, but I think it will be worth it. I am getting a Wilson barrel (#4) for it. Cut to length, chambered, fluted and threaded it was less than $500 from Ragged Hole Barrels. Considering I only paid $90 for the donor, even with a great stock, I am going to be into it for less than $1000 when all is said and done.
Oh, another tip on gauges, you can rent them from remearrentals.com for $7, plus shipping. https://www.reamerrentals.com/ProductDetails.asp?ProductCode=6x45%2Eg
