Hello
njc110381, it has been a pleasure walking the trail with you from your first post musing about a .458 Lott to do it all, to the actual ownership of this .416 Rigby.
This sense of camaraderie is emphasized, because I had exactly the same issue with exactly the same rifle
Here is mine:
Allow me to proceed by elimination. For my rifle...
1) No, this was not the loads. All the folks, you included, who stated that 10" groups are not an ammo issue are correct.
2) No this was not a bedding issue. The stock on these rifles is made by Bell & Carlson and includes a full length aluminum bedding block and aluminum pillars. The barrel is free floated and you can take them apart as often as you wish, they will come back to zero. For information the torque specifications are 50 inch/lbs for both action screws. Tighten the front action screw first after assembling the rifle and slamming the stock vertically on its recoil pad on hard ground to sit the barreled action against the bedding block.
3) No this was not copper fouling. I had not, and you have not shot enough for that.
4) No the scope did not give up the ghost. Mine is a Schmidt & Bender scope 1 1/4-4x20 30 mm tube.
5) No the rings were not poorly mounted. I used Alaska Rings correctly degreased, and correctly torqued for the big cam screws at 30 inch/lbs, the lower lock screws at 40 inch/lbs, and the ring screws at 35 inch/lbs. And I do use a torque wrench so the numbers are reliable.
6) No it was not me, although for a while I doubted...
And then...............
All of a sudden, after 20 to 30 rounds, I do not remember exactly, the rifle started grouping 1.5" at 100 yd. I was dumbfounded...
What is was, I discovered by chance when cleaning the rifle, was that the scope had been progressively sliding forward in its rings imperceptibly with each shot, until the shoulder of the rear ocular came to rest on the rear face of the rear ring. From then on, problem solved!
Until...............
I took the detachable rings off and put them back on. "Deja vu" all over again. The next group was somewhat larger (~3") and had moved something, I do not exactly remember, like 6" sideways and 4" or 6" in elevation. What the heck !?!?!?
This one took a little more head scratching, but I found out the issue. The ring mounting grooves on the front bridge are not milled all the way. Since they are milled with a round cutter, they end up in a radius. Conversely, the edges of the rings are square. As the front edges of the front ring were biting forward under recoil into the radiuses of the grooves, they were digging into the grooves radiuses irregularly and never came back in the same place whenever I re-attached the scope. This was solved by moving the front ring back about 1/4 of an inch to provide ample clearance for the radiuses.
Since then I have encountered no more "inexplicable" accuracy issue with the CZ 550 .416 Rigby.
I am of course not saying that this will automatically be the issue with your rifle, but I do suggest you check these out. What I am pretty certain of is that: something mechanical is moving. Options are limited: barreled action within the stock; internal components within the scope; scope within the rings; rings on top of the action.
Good luck and let us know how it gets resolved. I would take a decent wagger that it will turn out to be pretty simple
... in retrospect