Speedrunning is not a thing that should or can be stopped. All you can do is make speedruns take longer, and that is bad game design, especially when the solution to running the hallway fast is to put more locked doors in it. No, the way to stop speedrunning is to give people a reason NOT to speedrun.

My idea would require significant system-level changes but each dungeon should have a checklist of stuff to do.

Let's say Brayflox Story (because I firmly believe this is the best designed dungeon in the game right now) was tuned up to be an endgame dungeon and rewarded myth/soldiery instead of exp.
Completion: 50 myth + 45 Soldiery
Killed X enemies: 10 myth
Rescued all goblins: 20 myth + 5 soldiery
Opened all chests: 5 myth
Killed brayflox: 10 soldiery

It wouldn't kill speedruns. But it would give full clears a reason to exist. Also, the soldiery cap is far, far too high, and the myth cap should never have been removed.