Mac:
I would argue that they should all be built on the 12-bore action! The thicker chamber walls would put more weight 'between the hands', and allow the maker to slim down the forward part of the barrels 'correctly' while still keeping to the nominated total weight.

The result would be a rifle with the liveliness of a Jeffery or Westley Richards boxlock, rather than a lump of lead pipe like large-calibre conversions on the 16 or 20-bore action are prone to be.