Phase ships could probably use a balancing pass at some point, but they are likely to get special campaign-level functionality, so it doesn't make sense to balance them *now*. Some kind of campaign-level stealth could be worth a lot of traded-off combat capability.
That said, I think they're pretty good now, they just require a different approach. Like Thaago mentioned, they're best for taking on larger ships that they can outmaneuver. This does tend to limit the Doom's effectiveness, since it's not quite nimble enough to easily outmaneuver capitals (though it's still fast for a cruiser), and besides that, there aren't very many capitals to begin with. On the other hand, it's offensive potential is really high, so you can alpha-strike smaller ships effectively - it's just unforgiving of mistakes and requires more finesse.
The mission ("Ambush") is definitely beatable with the default loadouts, btw. Oh, heck - just did it now for fun: won with no losses on the second attempt, though both frigates (set to escort the flagship) took heavy hull damage.
They key is to identify the biggest threats and deal with them quickly. In this case, it's the enemy Condor - it's a carrier, and if it lives, the fighters will wear you down. A well-placed volley of Sabots and Reapers (with "Fast Missile Racks" if necessary) can finish it off. If you fail at that, though, you're not likely to get another chance.
The other high-priority target is the Enforcer. It can wear you down with sustained fire and you can't outrun it in the Doom. But you outgun it severely as long as your flux is still low, so the key again is to dispatch it quickly, which you have the tools to do. Landing the torpedo strikes is tricky, but the amount of burst damage you can dish out is staggering. What you have to avoid is a drawn-out engagement.
The Lashers and fighters are easy enough to finish off with your pulse lasers and the occasional brief phase in/out to avoid the heavier missiles. The Mule doesn't have the damage to be a real threat, but it's still best to finish it off with torpedoes because it does have the speed to stay with you and the shields/armor to not be easily driven back by pulse lasers.
Another thing that works well is to vent fairly early - as soon as practical after making a kill. You're going to take some damage regardless of what you do, but timing three 30% vents to avoid heavy damage is much easier than doing that for a 90% vent.