I don't think it's necessary to weaken or eliminate traits or special weapons or ANY of that stuff. I think the special maps would be fine as is, and still be fun. I do think there would have to be an element of randomness to it, to be fun, though.
First, I think the maps should be recreations of the original Doom. Second, I think there should be no "secrets" sections-- you could do speed completed, instead, or amount of map explored (I know, secrets and map explored are mostly the same thing), or something like that. In today's information age, secrets tend to get revealed really really really quickly, and that element of the game would soon be boring. Third, I think the maps might benefit from an element of randomness-- maybe place MOST but not ALL of the items (leave key weapons/armor/unique stuff in place) at random-- i.e. extra common ammo and small med-kits. Also, randomize the spawns of most, but not ALL, of the monsters-- boss characters or particularly out of place monsters would spawn in the same place each time (and would move to a random location via walking around). You could even go as far as to generate the monsters completely at random.
In gameplay terms, it would be like "The Halls of Carnage" with a Baron of Hell in the usual spot, but everyone else just splattered across the map.
OR, you could have each level have a PORTION of the map pregenerated, and randomly make the rest of the map level. I.E. when you get the message "you feel excited" you know the same layout room is going to be somewhere on the map. The game could use that same principle, but with a larger, series of rooms, each uniquely designed, with the same items/monsters/whatever each time.