Not sure how many were built - would guess at around 30-40? Hank Kaufman the designer.
In the vid NS33s (transom humg rudder, companionway offset to stbd) feature from 1:19 to 3:19 (sail 4521), 3:20 to 4:05 (sail M95) then the 31 from 4:06 to the end. Am pretty sure that all 31/310s had rudder hung off rudder post underneath the stern, probably with small skeg also. Believe all 31/310 keels were cast iron - would assume the bulbs were CI also not lead but not 100% sure.
Yes excellent stern space due to the beam - for cockpit and double berth under, also very easy to get on board through the transom.
Couple more good vids you have probably seen.