Some ideas:
Best control point map (includes TC and KOTH, excludes mvm)
Best payload map (both normal and race)
Best arena map
Best MvM map
Best other gamemodes map (modes like SD, RD or any gimmick gamemode people came up with)
Best detailed map
Best optimized map
Best balanced map
Best entity work
Best unfinished map (it has a finished alpha state but is fully undetailed)
Best gimmick (note the waiting moments in thunder mountain and barnblitz are gimmicks)
Best transition (the best reuse of a spawn when going between stage 1 and 2)
Best finale zone (final cap, bomb pit, hatch in mvm - simply the one with the best touch to it)
Best use of a new theme (themes barely in use by valve or other mappers, for example the hong kong, space, japanese, jungle and so on are fine for this - its a skill to design a new mapping theme)
Thats 14 potential awards of which only 5 should get a potential runner up to me.
I don't care if it's a popularity contest.
For a part i do. Popularity simply shows which maps are best accepted. For the first 5 awards in the above example the popularity should matter. For the next 5 things its more technical and doesnt require a perfectly built map. Popularity on those would be a very bad thing and remove all of its usefullness.
Even for our existing contests popularity matters alot. A map no one knows about could be perfect, but if no one knows about it... whats its use about it. Trying to do the effort to at least get your map known is vital. And when it is good it gets popular anyway.
Also, i think that 20 awards is fine. but not all of them deserve a runner up. Only for major categories it should matter, but for details it should not. If someone did some excelent entity work, the chance that someone equals it to begin with is minimal. Its not impossible, but im sure you arent going to get 5 diffirent mappers in many situations. That only happens with detailing contests in 72h format.
The requirement also should be that the map must be finished (except on the unfinished part - of which i would say it still can only be given once to a map)