CJF
"Е.just got back from the range and using the lower charge that Woodward said was used for regulation did nothing to improveЕ."
1) As I asked/hinted at previously, what BP are you using? The available brands are not all equal energy wise.
2) You have not said what weight of bullets are you using? Heavier than 340grains (maybe 350 grains) likely will be an issue.
3) Plenty of experienced guys will relate that it takes more weight of modern BP to equal the regulation & velocities gotten in the old days with the usual Curtis & Harvey #6 powder. I'd try to avoid 3F.
4) it is the case that often times you simply can't get modern weaker BP to give adequate regulation. Nitro for Black with H4198 can be your friend, besides that, NfB loads recoil noticeably less.

"Е..I really want to get this rifle and the Dickson to regulate with black powder before trying nitro-for-blackЕЕ"
-See #4 above

"ЕЕ.What was the standard regulation distance for 500 BPE?Е.."
1) Usual English regulation distance was 60 yards, sometimes more. Most guys these days use 50 yards.
2) You may eventually have to have a taller front sight made, or file the rear sight to lower the point of impact.
3) Maybe adjust your sight picture? (is the front bead buried at the bottom of the "V"?

"ЕЕЕ.But there's no moving the front sight and the rear is currently staked in placeЕ."
- "staked" does not mean immoveable, you can use a small hammer & proper brass drift to move the rear sight as necessary despite the witness mark.

Suggestion: If you do not own a copy; beg, borrow, or steal the book "Shooting the British Double Rifle" by Graeme Wright. It is invaluable for those that want to get good results with Nitro, Nitro for Black, and Black Powder in these rifles.

Good luck & enjoy the rifle, a Woodward is a real treasure that is relatively rare.
- Mike