If you do the old SAS 'piece of bungee over the shoulder under the armpit' thing, all you need is an open sided (facing forward) kydex clip, or loop of velcro, or (I think somebody still makes them) retention clip for breachers.
If you mount this to your plate carrier with the opening forward, you should have the shotgun tucked tight to your body, barrel down, and be able to just drop your primary and pull it straight forward and into your right hand (if right handed).
Same kind of idea as a shoulder rig for SMGs, but about 10x simpler. You don't even necessarily need the clip, but anything to keep it from flopping around is good.
For standard tri shots (and cqb generally) I also run a medium sized dump/ utility pouch right up front, on my weak side (right for right handed). Mags for sidearms eject straight into it, shells have inches of traverse, with the eventual purchase of a shell ejector (looking at the same as you) the shell catcher will open and dump straight into the dump, all in my workspace.
I wouldn't run a sidesaddle on a Breacher, but those shell pouches that look like sunglass cases are pretty good if they're up high and you only load a single row (5-7 shells). I have a huge folding shell carrier (it holds 30 3" shells or something obscene) that will eventually make it to the rig, but in playing around with it I can't see that it will be useful for doing anything but give me storage until I can bump them up to the "sunglass case".
Here's a video for your reference, skip to 3:58:
https://www.youtube.com/watch?v=1urLoqVZm70
Edit: that's if you're going stockless. If you're running a tube stock or something you're pretty much running a second primary and all that comes with it. I would personally look for an old 733 commando stock for a tube, or some kind of outside-folding wire stock if using a folder, just to keep it as slick and trim as possible.
For slinging it I'd put the SMG on first, rigged to clip or hang in front, tight to the body. IMO the shotgun is the tool that needs to move freely where straps are concerned; I don't want to deal with getting it fully out of the way and then back again if I'm forced to go to my shotgun, or need to pretend to ruin some door hinges.