Burness Corlett were producing hydroconic designs as far back as the 1954. In they UK, they worked primarily with just two shipyards - P K Harris in Appledore and Mitchisons of Gateshead - to produce tugs and trawlers using hydroconic hulls through the mid 1960s. They formed a limited company called Seawork Ltd for this work. There was one other UK yard that produced some smaller hydroconic vessels, near Southampton, IIRC, and then they licensed Adelaide Shipbuilders. The patents would have expired in the mid 1980s, so is that when the term hydroconic fell out of use, I wonder?
As for the differences between a regular chined hull and a hydroconic one, that's where I got lost! All to do with angles, curvature, positioning of props and rudders etc. It must have been sufficiently different for the patent to be granted of course.
The plans mentioned from MB magazine were for Dominant/Diligent. They stop at the waterline, with no underwater details given at all. My GA plans for Meeching only hint at the chine lines. Burness Corlett's secretive influence, most likely!
There is one unfortunate characteristic of the hydroconic design, in that the vessels can be lively, even in a slight sea. I was once talking to a North Sea trawler skipper who described his hydroconic hulled trawler as 'hydro-comic'! However, although they'd roll and pitch like crazy in foul weather, they had the happy knack of always rolling back upright, even after a 40+ degree roll. My Dad did a salvage job in Meeching, in a F11 storm and said that he always had confidence that the tug would be OK, a sentiment echoed by his successor as Master, who said that she would always bring them back home, whatever the sea threw at her.