No one trying this one?
I don't have a double of any type or side by side "cape gun", but do have a Brno ZH304 O/U in 7 x 57R over 12 ga.. Generally I stick to a factory duplication load based on an old NORMA loading table I've had for about 40m years. (Alternatively I look for 7 x 57 STARTING loads in a loading manual.) It matched the factory iron sights. For the Zeiss/Jena scope, the adjustments are aesy if "fiddly". My grouse potting loads with cast bullets @ about 1200fps hit a bit low & left. I just hold off, if I remember ! O/U Rifles also need regulating, (see below) but as the recoil is straight back the variables are probably less.
From what I've read, side by sides are very sensitive to bullet weight, and load, as the recoil doesn't come straight back through the stock. You are OK if you know what load your gun is "regulated" for (that means it is actually shot in for a specific load at the factory.) This is a very time consuming (read EXPENSIVE) proposition. To duplicate the load the gun was rgulated for is less of a trick if you know the details of the factory load, especially the bullet weight. I recall an article referred to in an ancient Gun DIgest. I think it was Elmer Keith. As I recall, heavier bullets shoot more away from the center line than lighter ones. Powder, load, and velocity, have an effect, but I can't recall what, so I won't venture. Cheaper guns might not be carefully regulated, so finding a load will be an adventure. I have read of some doubles shooting tightest with different loads in each barrel.! A Cape gun gives you only one barrel to sight in, and ther might be some adjustment to the sights. I'd keep loads modest as I went along.
Good Luck!