in the moderate Aristotelian city

Something we stumbled into on the primeval_denial comm which did exactly gamify without introducing competition, was to introduce icon prizes in return for achieving goals set yourself. The denial community only does this for a month at a time, with a table set up in advance to pick the icons from (here's an example of an old table). You'd need to adapt the format but I'm sure you could manage something similar if you had a team of people prepared to make stuff for other people who had achieved self-set targets.

I'll happily make icons and, in some cases, larger graphics for instance.