Well I just got a message from the Custom Shop/Precision Center at BFR that has made me a very happy camper. They can machine an octagon barrel and leave an inch and half or two inches round at the end of the barrel. I have requested the underside of the back-edge of the rounded barrel be measured so that the ejector tube is trapped between it and the back-edge of the frame where it originates from. The front rounded barrel portion should extend forward enough to allow the front-sight base to be fully supported. This would determine the total length of the barrel, most probably approximating 6.5 inches or so. Using a Bisley BFR grip would seal the deal for me. At roughly $2200.00 it is not cheap, but I never expected anything less than precise craftsmanship from BFR.

Move this to Shooter's Bench please. I posted it to Handgun Hunting and that is the not the right Forum. It should be changed.

I guess I'm not the only one with such tastes.
I dropped my BFR off to JRH for just such a profiled barrel. Mine will end up at 6.5".
I machined such a profiled barrel for one of JRH's customers about 10 years ago and it looked sharp. We called it a 'banded octagon'.

It is called a banded octagon? I just could not get BFR to put a band on one of their regular revolvers. By recognizing the octagon would need to be machined in the Precision Shop at Magnum Research, I asked if they could just stop machining the octagon about 2 inches from the end of the barrel? The Custom Shop said sure and the measurement that must be precise is the inside corner that traps the ejector rod tube under the barrel. I called JRH and they said they could do it, but I would rather have BFR do the work in house.

Yep. It is a little time consuming to machine / finish that octagon profile.
Since the top flat of the octagon has to be timed so it is perfectly parallel to the top of the frame, the barrel shank has to be trimmed for the cylinder gap .002", and to trap the extractor housing between the band and the frame. Then to draw-file the machining marks off the flats so you have sharp parallel points on the octagon and keep a sharp banded shoulder. This is all done without final tightening the barrel to the frame. Round barrels are so much easier because the timing issue is much less critical.
There is also the work on the extractor housing. The inside radius that hugs a round barrel has to be machined flat to hug the flat of the octagon. Since each caliber barrel may have different barrel diameters, the extractor housing not only has to fit inside the round hole at the front of the frame, but also fit flat / parallel to the flat of the barrel.

It would seem turning a round barrel down and leaving a barrel band remaining would be much easier to deal with. In fact, looking at the octagon treatment BFR Custom performs the barrel that attaches to the frame is left full round and seated into the frame and the octagon flats extend out towards the front sight. So just taking a round barrel and turning it down in the middle but leaving it full size on both ends would be the way to do it. But I do not think they want to do it that way.