I came to the same conclusion re the 3"3/4 CHOKE (as it appears on the barrel), as actually meaning 3,3/4" chamber.
Because the proof marks for both barrels are 8/1 this points to them being .847" bore (9" from the breech), rather than the standard .835. I don't have any socket tools of the right diameter to check/confirm this, (see above), but will look for one shortly to measure the bore. However, using just a dial caliper as a very rough guide, the chokes seem to be Full and Extra Full, which is not unusual in a dedicated wildfowling gun. I wouldn't use steel shot in any old gun, especially one with tight chokes, but I do have a supply of bismuth and also Tom Armbrust's book, "4 and 8 Bore Shotguns and Loads", which has various load recipes for industrial shells. I'll need special swaging tools to make industrial cases suitable, but C-H Tool and Die seem to sell them as does Clays and Game in the UK.
The best news is that Canada geese in New Zealand are no longer subject to the rules around non-toxic shot. So there's no reason not to use lead BB's.
