For training purposes -- since I think it's too rocky where I live to shoot high-power rounds close to the ground in front of you, and the only place I could shoot one in multiple directions would be down in a draw -- again, pretty rocky. What would be the closest shotgun/calbier combination as far as weight/balance -- I was thinking 416 Rigby/410 -- but that's based on nothing other than a similarity in dimensions.
Essentially, I was thinking if it would be possible to use your double rifle on rabbit skeet/other positions, and not have the effects of the high-recoil/worry about where the bullets are going -- it should really improve proficiency.

Hmm... I'm not sure what you are getting at here, but here's my guess... Since you're not going to find many 10-12lb shotguns, "practice" would be mainly, point shooting instead of "aiming" precisely. For getting used to the weight and recoil of a double, I bought an A-Square hannibal 11 lbs with scope, just over ten with the open sights, chambered in 470 capstick... DR type recoil, but at about $4.50 a round instead of 9-10 a round for my 475. The sights are very similiar, weight is right on, balance is a little different, but I can pull out one of the mercury reducers from the butt to make it a little more barrel biased. I'd shoot solid cores, since the price per box wouldn't be much different from softs, and they should poke their way into just abount anything you take aim at without much ricochet...

If this isn't what you were looking for, clarify your topic..

Sorry, I kinda thought that was as clear as mud.
A) You can get shotgun barrels for a double rifle
B) Which rifle caliber would have a set of barrels that would balance the closest to a set of shotgun barrels?

I know the unmentionable caliber and a 410 could balance very closely. My idea behind it would be able to use something which would balance the same as a double rifle to shoot skeet, etc, and as such, get used to snap shooting, swinging, etc w. a double rifle.

I have some lovely, to me at least, SxS shotguns which handle NOTHING like a double rifle -- admittedly I haven't found a Searcy, or Chapquis to try yet. Just the ones that were at the SHOT show -- I might have to ask this more of the local Limey gunsmith.

I liked the idea of a lower practice recoil, since it would allow more rounds to be fired, and help to prevent developing a flinch.

I'm with you now. Yes, a 410 would provide you with the smallest bore (obviously) relative to the barrel profile... which means more steel in the barrel walls and more weight.

However, extra barrels are not inexpensive (typically around 50% of the cost of a new gun) and a 10-lb 410 would be tough to justify - especially for practice.

I'd reccomend reduced cast loads. You can have all the practice you want to get familiar with the gun at a reduced recoil level.

As for the distance the bullet travels and you wanting to shoot shot instead of a projectile, two things come to mind.

First the obvious cast bullet, which is softer than a jacketed bullet.

Secondly, some type of chamber adaptor that would allow 410 shotshells to be loaded into a larger chamber... don't know that I would do it in my gun, but if your DR bore is large enough - it's certainly possible.

I can't imagine how it would do any damage, but the melted plastic from the shot cup would probably be a mess to clean from the bore.

I have a set of 12 ga barrels for the Searcy PH 470 NE. Balances about the same and I have used them for just the purpose you have thought of. Try setting the traps to throw the birds at you but angled off to the right and left. Faster than buffalo. Only difference is that the shotgun barrels don't have sights. I might fix that

My Searcy 470 PH weighs 9 lb 8 oz and the 12 Ga barrels come in at 9lb 2 oz. It is great practice.

One of my buddies has a rifle that can chamber 410s -- didn't hurt the gun/cause any melted plastic, but doesn't pattern worth a darn -- best guess is the rifling bites into the wad, and gets it spinning/slowing down relative to the shot, and just messes everything up.