He gained interest in the world of fantasy creatures as a child through the TV show Kukla, Fran, and Ollie, and the film King Kong.
[1] Conway worked as a social worker for four years and then went on to design for a leading toy company.
[5] Conway led the design team on Disney and Walter Murch's film Return to Oz.
[8] Conway described it as, "one-fourth the work of The Dark Crystal at ten times the speed",[8] where they created six creatures in fourteen weeks.
[5][9] Conway created the animatronics used in the TV movie Red Crow and the Ghost Ship.
[5] Conway worked on the TV movie The Murders in the Rue Morgue as a puppet designer and creator.
[5] Conway worked under Frank Oz on Little Shop of Horrors where they created and designed the Audrey II puppet.
[10] In the designing process, Conway and Frank Oz had conflicting ideas on what Audrey II should look like.
[10] Conway began creating Audrey II through the creation of working prototypes that they named the "Feed Me" Plant.
Because of this Conway pitched the idea of having the actors act in slow motion and to speed it up in the final cut to make the puppet more fluid.