The DT on the last part isn't a viral anything - it's an aura that pops on you once you enter inside the the inner ring/room. You can easily pop back outside through one of the doorways, watch it drop from your buff bar, and then pop back in to keep killing. I can't imagine how long that event would take if you ranged it .... *shiver*
Here's another tip... look at the stacking on the room DT - basically, if you have any recourse-type spell on you already it'll block the DT from holding on you until its over. That means bard Lyssa, cleric promised line, druid promised line, etc, etc will keep the DT from landing on you for however long it's up. For a bard right now that means 50+ seconds without the DT clicking down at all, plus the 30 seconds or so you get to stand around before it actually fires. That is a lot of melee dps time.