I have generated some data that I would like to share with members here in hopes that it starts some discussion and helps me process what I think is going on.   
I built a 38-72 Win on an original high wall using a barrel from RKS - it's stainless, 31", gain twist, exiting at 1:15.5" twist.  I contoured the barrel to half round half octagon, breech across the flats is 1.110" muzzle is 1.080".  I made the chambering reamer following most of the specs of the 38-72 Win with the exception for the rim, made it to fit 9.3 x 74R Horn. brass.  Headspacing was to my preference.  None of this is really consequential as the rifle when i do my part is really beginning to perform, not that it didn't from the get go.  Initially I was using the 313g RCBS BPS with 27.1g of IMR 8208 - I'm not going into the rest of the cartridge load config as I experimented excessively, and the lab radar promised exceptional results... 
I did some initial tests on a calm day, had moa and slightly less at 100 yds benched.  Hit the target fairly consistent at a 1000 yds - thinking this is going to be sweet.  Good velocity, nice groups, pleasant recoil, - all the misses would be mine 
Shot a match with some moderate to intense wind a month later, WOW! had 28 minute groups at 900 yds a little less at closer yardages but DARN!  My knee jerk reaction was change bullet and revisit the powder choice.  Thought about returning to black but decided to give my standby smokeless a try - 5744.  The bullet choice ended up being a "money"  .376" 360g from BACO.
I put together about five different loads, discovered those that were close, tuned them within a tenth or so, mounted a temporary Leupold to eliminate some of the iron sight flaws, etc.  Latest results at the range were 5 shots well sub-moa.
Shooting at 800yd in 15-18 mph and some gusting wind at 9 o'clock things appear to have settled down.
So, in lieu of details given, I was shooting a gong at 500 yds last weekend, winds were shifting from my 3 - 5 o'clock.   I didn't have the Kestro with me but I'm guessing 8 to 12 mph.   My hits were consistent, I was pleased with the results. 
When I went and picked up the gong and was loading it in the pickup,  I noticed the impact points within the splatter.  A couple were centered, but the majority were located around the edge.  Nothing consistent or constant.   Does this correlate with Dr. Manns reference to oscillation.   Can't wait to experiment more, anyone else seeing this?  Attached a few pix.

I'm liking the velocity, 12 shots the average was 1281 fps, the extreme spread was 18 fps.  Calculated BC with velocity 0 to 100 yds   had .498.   higher and lower velocity and my BC dropped, a change of 100 fps faster and the BC went to .39 - and the group increased.?   
I agree, more rounds down the barrel.

John, 
The gong is a swinger, the bracket is bent (adjusted) so the plate hangs perpendicular to terra-firma.  It's also 46" diameter 3/8" 
Thanks,
Greg

Just guessing, but looks like the egg shape is consistently toward the bottom.
Bullet leaves the muzzle in an upward arc. Gyro spin is keeping the bullet in that orientation until it strikes the target.
Opposite from tipping instability. Just a guess and not a bad thing.
Chuck

Chuck, the splatter did vary but if you notice the dot inside the splatter, that's what got my attention.   I have pictured - one at 7 o'clock, another at 8:30, one at 1, of the fifteen or so I shot, two were dead center, the other dots from point impact were 3, 5, 12, 6, etc, no real rhyme or reason I could see.    
I have a match this weekend but following this, I'm going to return with the gong, see what the markings are at 300, 400, 600 thru a thousand.  Is the bullet "sleeping" or is it just on the verge of stability?  I'll take the paper frame out and try it also.
   
John Boy, I did the paper test on the rifle build just before this one, a Hepburn in a 40-82.  I don't recall an off center impact mark on the plate with this rifle.  The paper at 3, 5 and 6 hundred showed very little tipping or oscillation.  It shoots well but after 75 rds. or so I start to feel it so I'm dabbling.

I'll have more thoughts about performance after the weekend I'm sure.  Most of the performance issues will be a result of the guy jerking the trigger - that's the norm.   These impact marks just raised a few questions for me.  I attached a couple more pictures.

At long distance every bullet strike will be at an angle. I'd guess the arc of flight for that velocity and bullet caliber/weight would likely be 30 ft. at 500 yds., and probably twice that at 1,000 yds., so regardless of the plate hanging perfectly straight, the impact will be at a slight angle.
But what is curious is the impact shown are not all the same in comparison to the splash. Some hit high, low or center. So likely not caused by angle. Wish I could tell you what is causing it, but I'd not be too worried unless group size opened up.

marlinguy wrote on Sep 11^th, 2018 at 7:33pm:

When I was calculating sight settings for quite a few guys out to 1,000 yards, the typical midrange was 55 feet for 45s.

Chuck,
I just re-read that last evening in Mann's book and Pejsa had more info than I could digest late last night, it's possible.   
I was trying relate it to the cast - bullet imperfections, cartridge alignment, hold, phase of the moon, effects of the hurricane in the Atlantic and Pacific at the same time?  I was shooting due south with a right hand twist?  I really need to finish my rifling machine - then I won't have any time for work... 
 
I have cast these considerably harder than my norm and I won't debate the argument about black vs. smokeless.  I've known a few that shoot smokeless that with their combination I haven't seen the likes of someone shooting black even come close - the results didn't come as easy as it does with black.  I use the phrase often "this smokeless stuff is just a passing fad" just to light'em up - and I have to eat that black bird quite often.

Thanks everyone for the responses.

We'll see what the weekend brings - carrying a spare in a 45 just in case I need a sanity check. 
Greg