Well I have now been out four times with my own loads. Concentrating on the advice above:
1) Tightened the necks by sizing with a 30-06 size FLS die; thanks Huvius, very successful.
2) Shooting offhand with barrels gripped well forward.
3) Got a couple of other experienced members to also shoot it. One who sweetens his days with a .500Nitro said it has no recoil at all! I think that is good testimony to the combination of lighter bullet (300gn), reasonable weight of rifle and lovely English stocking with some cast-off and a wide buttplate.

Here is the usual result, left and right barrels on an air pistol target shot offhand at 25m:

The sight picture requires the bead to be at the bottom of the deep V rearsight for these little aiming marks. I find the trigger pull crisp and responsive, most satisfying. I wish I were a better shot though!

Next: more projies, I shot off all the jacketed ones. Magnum primers and maybe some filler to reduce unburned powder.

I had one of my guests filming video as I shot it and she clearly said: "That is a MANLY rifle!"