I would absolutely follow the advice of "Connatter" and check out Alamo Precision Rifles.
For the record the only dealings I've had with them is the direct purchase of one of their APR actions. I was looking for a Defiance or Borden, but it was gonna be several months before my builder could get what I needed. So I took a chance and bought the APR for $400-500 less than some of the more popular customs.
My builder paired it with a Bartlein barrel, AG stock and jewell trig. in .280ai. Now after 45-50 rounds down the tube it's proving to be a tack driver......2's and .3' every time. The action is smooth and flawless mechanically.
As for their complete builds, I am consistently surprised by the cost. I just had a 6.5 built by McWhorter, who has earned their stellar reputation. And it's everything I expected and then some. It was also rather expensive. They do go the extra mile and develop a load and send the rifle with a decent supply of hand loads.
Just as I was receiving the rifle I looked on Alamo's site at their "rifles ready to ship" section. They always have 4-5 complete builds ready to go, and they usually get scooped up quickly. Anyway, they had just posted a 6.5prc with the same action (defiance), same barrel (proof), same trigger (trig tech)....the only difference was the stock, but it was a McMillan just like mine. The other big difference was the cost.....they had theirs listed for $3995. Safe to assume that I paid quite a bit more......even after I got the repeat customer 10% discount. I did get the load dev and 40 hand loads, which is worth a good bit, but my point is Alamo was selling their product at a very very friendly price point.
I can't speak to their lead times on complete custom orders but they would be on my short list. It won't be long before their work has earned the reputation, like McWhorter, R bros, Lane, etc, to charge a premium.