I had this problem as well the other day. It was the first time I'd played the mission in months, and I was doing it with my KDF character. I ALMOST managed to beat him and the demo guy straight up without dying, even though I was VERY surprised when I popped at the turbolift rather than in the office.
I actually DID drive Kara'Kan off and defeat the demoman, but it was a mutual kill, I shot away his last HP just as the grenade he'd thrown went off just a little too close to me (I'd -tried- to dive out of the way, but got hung on a table or something.) And I had no shields left and half health.
So yeah - ouch. Re-spawned to the empty command center and then beamed up to my ship. I did something wrong there as well and died once, but I think it was just me not keeping track of shield facings in the furball.
I do want to say - I LOVE everything that happens up to the Command Center fight.
I've done this set of missions twice, once with a Fed Captain, once with KDF. But both of them were Tactical. I have one Science Cap I'm about ready to do this with, and I'm looking forward to seeing how differently it plays.
One piece of advice - if you're a Tactical Captain.
If you can, get yourself the Tactical Kit "Operative". That's the one with the personal cloak. Use personal cloak/invisibility and it'll make your life a LOT easier during the promenade section. Just be warned, using lifts and access panels will drop the cloak. So you'll have to fight any Jem-Hadar close by. But it definitely cuts down on random fights on the way. I like having the tactical advantage of being able to pick and choose which fights I want to get into.
(Heh. Nothing like the adrenaline spike that occurs when you "bump" into a Jem-Hadar who is also cloaked.

"ACK! Did he see me? He didn't see me.... WHEW...")

TF2 SPY: "It seems I am not the only spy around!" )