I have a 7x65r and 16 bore combination. The 7x65r will do pretty much anything that a 30-06 / 270/ 7mm R.E.M. Mag will do. I have used it to take red and roe deer out to 200ish yards. I have shot it out to 350 and was repeadidly hitting an 18 inch sized rock.

A 16 bore slug certainly will act as a good stopper, but so will the 7x65r.

Norma load a 170gn oryx at 2650fps https://www.norma.cc/en/Products/Hunting/7x65-R/Oryx1/

Or 156gn at 2720 - https://www.norma.cc/en/Products/Hunting/7x65-R/Oryx/

With those or equivalent from RWS or Geco or Hornady it will put most things on the deck.

Please do get a rimmed calibre - a break action needs a rimmed cartridge, and to reload the empties just fall out.