If you're playing a DD, I'm not entirely sure that MR is needed, since they get +6 per level. Maybe one MR source if you want to have a flat 0% chance of confuse/paralyse, but you're pretty close to 0 automatically.
My record is 40k turns for 15 runes, which is probably pretty close to the 30k for 3 rune timeframe. Really the #1 thing is to just keep diving. Try playing a game where the rule is you have to take the downstairs as soon as you see the third stair. Obviously the more aggressive rule is to take the first downstair, but that can be very, very intense. Feel free to take it somewhat slower for the first few dungeon floors, as they're the hardest. But if you feel "above the difficulty curve" you can also ramp up the rate at which you dive - take the first stair down right away. A good example of this would be a DD who gets a vamp axe or otherwise very strong axe, maybe a good trog gift or you find your first battleaxe after having to use a hand axe early game. Or for a VS, once you get statue form online, you now want to dive the next several floors/branches quickly because your power level just shot way up.
Not autoexploring and having a good idea of how to walk around a level to expose the most area/not have to backtrack is also big, but I'm personally too lazy for this - you only need to do this for extreme high scores. You can get to 30k 3 rune wins by autoexploring as long as you are diving aggressively.
Also pick a branch order that minimizes backtracking - consider doing orc first, then running lair and doing the rune branches without leaving lair. Or skip orc entirely - it's not required. Likewise with elf; crypt you need to go through somewhat at least for tomb, but you certainly don't have to clear the end vault of crypt if you don't want to. Again, 30k 3 runes is a somewhat forgiving pace, so you can do the end vault for the loot if you want to.
This isn't necessarily the fastest order possible, but the order I took was Dungeon until orc (d:11), orc, then find lair (was also on d:11), lair, snake, shoals (aka lair branch 1 then 2), dungeon until vaults is found, vaults to 4, crypt, tomb. Yes, tomb was my third rune, before the vaults:5 rune. This was a VS with statue form, and before the removal of stairs in tomb. Then finish vaults:5, backtrack to slime, then finally enter depths for the first time. Pan -> exit through the abyss for abyss rune, then hell, then zot and escape.
There would be several shortcuts you could take to make that above order more efficient - go to slime immediately after shoals to avoid running back, completely skip orc, etc. You have to balance how strong you think you are with how much you're willing to walk backwards. Backtracking from vaults:5 to slime instead of doing slime when I was still in lair seems like it added approximately 700 turns to go back and maybe only around 400 to get back to depths afterwards. Hard to know exactly from just the morgue's notes, although if someone wants to watch the recording and get an exact count, let me know
Roughly +1000 turns for not being willing to take on slime at level 20 or so.
Obviously you don't have to do slime for a 3 rune speedrun, but it's an example of branch ordering being important to consider, and you generally have to take the closest branch, rather than the easiest branch.