In general the answer is no, you can't primarily heal t2 dungeons without some help unless you or the tank seriously overgears them. That being said, there are builds like the so-called Senticar that put out some single target healing while also having Justicar abilities. But these builds still typically rely on spammed single target heals from Sentinel to keep a tank up.
The reality is that the Justicar's healing abilities on others come from three sources: Righteous Mandate amplifying Salvation, heals that use Convictions, and Reparation. So let's take a look at each.
Justicars have an ability called Salvation. Untalented, it gives you a 40% chance to heal yourself for 10% of justicar abilities and 5% of other abilities. Talented this goes to 100% chance to heal for 25% of Justicar abilities and 11% of others. A Cleric with 14 points in Justicar can cast Righteous Mandate on one person. That person receives any excess healing from Salvation. In other words, if you're topped off, you're popping heals on your Mandate target that are basically equal to 25 or 11% of the damage done, depending. This is obviously FAR less than a Chloromancer.
The second form of healing is from Conviction-based abilities. For healing others, you're looking at either Loyalty (a 10 person, non-smart heal that heals the 10 closest players for a significant amount instantly), Bliss (heals you, waste of time), or Righteousness (heals your Mandated target for a bit more than Loyalty due to a higher base value). Each of these three Doctrines scale in the same way, meaning the only difference is base heal value. Spamming Righteousness on a tank is a better bet than spamming Loyalty, but only if you're only really trying to heal the tank.
The third form of healing is from Reparation. Reparation converts 25% of damage done by Justicar abilities and 10% of all other abilities into aoe healing centered around the Justicar.
So now with that out of the way... You can see that if you want to heal how you'd describe, you need to both amplify your damage AND amplify your instants.
I run a fun melee 32inquisitor/20shaman/14justicar hybrid that can put out some very good aoe healing, but for single target healing I would probably go a different route. My melee hybrid aoe healer is pretty good at it's job, though. I have several macros for different situations and if you're curious about the build, let me know.
There's an alternative called "inquisicar" which is a ranged aoe healing support build. Again, nothing like a primary healer, but it can generate convictions at range and pump out some decent AoE HPS.
I've recently been discussing with Lybra an alternative spec that would go deep into Warden for Overflow because a high crit rate + Doctrine of Loyalty should proc a ton of Overflows. The advantage here is you gain 15% to instant heals, and 15% to HoTs. You could maintain a stack of soothing stream on the tank. But ultimately this is way more of an aoe healing spec idea...