Trapdoor is hard!

I am surprised that your offense plus -Regen and -Res along with a Hardsuit didn't top the roughly 160 DPS equivalence need to defeat Trapdoor. Did you stick to him, or chase his clones?

In the general case, if you can't locate and take out a clone in less than about 15s on average then chasing the clones is likely a waste of effort. As for ignoring the clones and concentrating on Trapdoor... if you can't beat him in less than about 60s then it's too late and you'll start losing ground when he summons the 3rd clone (at that point his Regen rate goes up to 186 DPS and if you had that much DPS he'd be beaten already).

That's the general case though, for a Dark Def beating him in the first 30s or so is the way to go, since HT eliminates 1 clone's worth of Regen for 30s, meaning chasing that first clone accomplishes very little. Let's see, that leaves you needing 4016 damage (assuming he's L50) in about 26s (it'll take about 7s to cast Tar Patch then Howling Twilight). That's 154.5 DPS, with Tar Patch's -30% Res a raw 118.8. Then add his Regen at 11.6 (ignoring fluffy's -Reg from a random Twilight's Grasp). That's a DPS of 131 or so needed to beat him before the double whammy of a 2nd clone appearing and HT wearing off at around the 33s mark. I would have thought a Hardsuit and red pills would be enough for that (I'd would have estimated at least 150 for that combo). Sorry it didn't work out.

Howling Twilight does the equivalent of 58 DPS for 30s to Trapdoor while he has at least one clone out and 11.6 if he has none (assuming there's no other -Reg). If he has 1+ clones roughly half the time that's equivalent of a tidy little 35 DPS 30s DoT. If you're chasing the clones the key is actually defeating them quickly (as that both reduces the Regen he receives from them and gets you back to damaging him) but immobilizing Trapdoor and knocking off that much Regen adds a significant margin for error. Probably as much as adding a Hardsuit pet does.

I think for her, it might have been chasing the clones (or spending time on non-damaging actions in general), that did her in.

Either way you approach Trapdoor (you're down to just two choices solo without the lava or the ability to mezz him), I think you're right on the importance of HT for a Dark Def. You either need to leverage it for a quick win or use it to provide the margin you need to spend the time hunting down the clones.

He has normal EB mez protection. No more, no less. You need to stack 7 Mag or more to mez him.

Fear won't slow the recharge on his Bifurcate power nor will it stop him from using it when it is recharged, though it may delay its use briefly (up to 5s I believe) until he has a chance to act.

I stuck to him because see below.

I stayed on him and used gloom, dark blast, tenebrous tentacles, and nightfall.

It takes too long to defeat the clones, as in he'll summon another while I'm killing the first. Perhaps with inspirations I could do it, but it seems like it'd simply make things worse over the long term.

He didn't have three clones up at 60 seconds. He actually didn't get his first clone up for some time because I had him held, but he'd break out of the holds long enough to summon clones later on.

It wasn't enough. What can I say?

I don't know where you got this idea.

This is what I did in no particular order:

Gloom
Dark Blast
Tenebrous Tentacles
Nightfall
Petrifying Gaze
Twilight Grasp
Howling Twilight
Tar Patch

I am not new to this character; I made her in early 2005. I know how all of my powers work and which ones to use to boost damage output.

Petrifying Gaze was holding him until the dark servant stopped using PG or started missing him (I'm not sure which).

I didn't hunt clones, as I said earlier I found it to be a waste of time. If I can't defeat him in a minute, there's no point to continuing. I didn't actually spend all that much time on non-damaging actions that could possibly have been spent on damaging actions.

Necro/Dark Mastermind > Dark/Dark Defender in a solo situation by a wide margin. Dark Miasma is powerful. Dark Blast is not.

I kept him mezzed for a time, but he kept breaking out and bifurcating, so trying seems like it was a waste of time.

His Bifurcate power recharges while he's mezzed and and if he breaks out he'll use it as his first action. He also gets the +Regen buffs from his clones while mezzed unless he's Confused. So most hard mez needs to be kept on him at all times to be really effective. It can, of course, delay his use of the power even if there are gaps, but that will be the extent of it. If it's not complete coverage it ends up just being a sort of Slow effect. And that's probably not worth the effort with the exception of delaying that 1st clone.

Dark Blast is pretty weak against single targets all right. Gloom is the only really good damage ST attack. It does about 60% more damage per second of activation than Dark Blast, about 90% more than Life Drain and roughly 185% more than Tenebrous Tentacles and Night Fall. So using it as much as possible ups your DPS considerably. That's probably why Uber's high recharge build had so much more success than you, with the extra -Reg from having HT up more being just an added bonus. The key to any Dark Blast Def (or Corr) getting decent sustained ST DPS is going to be reducing the recharge on Gloom as much as possible and avoiding using the AoEs as fillers if you can.

Despite some unhelpful comments to the contrary, Trapdoor really can be a pain for some builds. Especially now that the lava is gone. The problem is that you really need sustainable mez for the tactic I call "Bind-and-Grind", burst ST damage and either range or mobility for "Clone Wars", or sustained ST damage for "Steamroller". It doesn't sound as if your build can provide any of those.

Just write off Trapdoor as your nemesis and move on to something your build is good at. Even the ease (though not rapidity) with which you'll be able to beat the Minotaur should restore some confidence in the build.