I know this is an old post, but I feel it's worth mentioning for any who stumble upon this that PVM times including Elite Dungeon runs are tracked on the PVM Records site. They don't track trilogy runs to my knowledge, but for those looking for records for PVM in general it's definitely worth looking at. My personal opinion, speedrun.com records for Runescape are probably better focused on non pvp content.

I've finally made an account on this site since I'm starting to get back into speedruns for various games, and of course I had to check out the available categories on RuneScape. PVM Records tracks speed kills and I was expecting this site to track other things like repeatable quests. But apparently the only quest related runs require you to make a new account. I check the threads and find this post, and either the categories were subsequently removed or never actually added in the first place.

So, I think it's worth reviving the notion, because there are multiple replayable quests that would make for a good speedrun. Perhaps among the most notable are Broken Home, which tracks your time in game for Maria's challenges, and Sliske's Endgame, which is possibly the most difficult quest in the game at the time of making this post, and thus would make for a potentially competitive category. If I had to choose only one replayable quest to get its own category, I would choose Sliske's Endgame, because it has everything you could expect from a grandmaster quest.