well i don't think of myself as a warmonger, but i probably win by conquest more than by space race. i almost never go that long. diplo and cultural are most common for me, and space race least common. i've only had one domination game in the recent past but i think more over time than space, and i literally can't remember the last time i launched a ship in my own game. i did in an SG months ago.
i only ever won by time once. for HoF you need a win of each type. difficulty, settings etc didn't matter, just no cheating, but all victory types have to be enabled. winning by time without triggering the other conditions can be hard work! i hit domination a time or two before i posted asking for help in getting it done. in the end, i did it by playing OCC, that guaranteed i wouldn't hit the dom land area limit and that i wouldn't accidentally have 3 cities go legendary. i basically harassed mehmed endlessly. i was shaka and had dancing impis sitting on every tile in his fat cross forever. i think he wanted me to finish him off, but i couldn't, the game had to last until 2050 so that i could get my checkbox *giggle*. poor guy didn't realize he'd be stuck with only one city, he didn't get the luxury of building oxford with only one university like i did, etc. actually i don't think he made it as far as education in the tech tree! i played on settler level, duel map, it was very silly and quite fun!