OK I built new designs, fighter, frigate, and cruiser. Used beam weapons and avenger missiles, and added on engine element. Both the fighter m0 and frigate m0 turned up as expected in the list of available designs, and I could select them to build. But the cruiser design did not. I don't know why; but I suspect I hadn't researched enough techs. I had the cruiser tech that allowed me to select the hull, but, apparently, not use it.
I will supply a save file if that would be useful. Just have to remember how to save stuff to the cloud.
(added) apparently I needed "battle cruiser doctrine" before I could build cruiser hulls. Well, the ship designer shouldn't allow one to design a ship that one can't build - or, better - the fact that one can't yet build it should be clearly stated and the needed tech (or whatever) should be stated.