Welcome Kappa.
Let me preface this with - If someone asks me for advice, I don't tell them everything that's wrong.

I am also a sxs person and given the choice I doubt that I would want anything else. That being said, trying to find one that even reasonably regulates both barrels with slugs is chance at best.

There are quite a few sxs out now that are set up specifically for this and they are typically upward of a lb heavier than they should be in most cases. Good to use like a rifle, lousy for bird shooting.

If you wanted to go by way of an OU the options are certainly greater because there are many available with an extra set of barrels.
A nice European rig with both barrels (probably in 16ga) sounds good.
Winchester made theirs in a number of dr and combo chamberings including 7x57 and 7x64.
Although I am not a tremendous fan, the Valmet can cover all bases and can be found with double triggers in an endless variety of combinations and they are a workhorse.
Had a BRNO 301 which was ok as a shotgun (fxf) and a rifle (slugs and 7x57r) - but just ok. Sat in the hands like a brick and it was gone after a few years.

Another option is to have a sxs regulated for slugs, which would also let you use it as a bird gun without loosing its effectiveness. While you are at it, have a second set of barrels put together in something large enough to cover the game you are interested in. (look into the gunsmithing forums)
Although it isn't factory, it would also be cheaper than another higher end piece in the rack.

Mind you I have never hunted anything that could eat me, so the comments above regarding the bolt action 375 or the lever 45-70 could be far more appropriate to your situation.

The single shot is up to you. Nothing better than a light stalking rifle when still hunting whitetails (and I am sure any other ungulates).

Drillings can be tough, as can cape guns due to the way they are balanced, but they do have a certain cool factor.
If I make it out for Sika this year, you can guarantee that with a 6.5 or 7mm and 2 loads of oo buck, range will not be an issue.

Good luck with your decisions, but don't be surprised if you end up with more guns than you already have (and you join the ranks of a number of others posting to or reading this)

Cheers

Tom