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It's possible. A key factor, at least for me, is the use of Crowd Control whenever possible. If a THM/BLM is in your party, ask them to use Sleep to lessen the damage on the Tank, and lessen the burden on you, the healer. If there's no THM/BLM in your party, then you, the healer should use Repose for Crowd Control. Granted, there are some groups where mobs are fully resistant to sleep, but if they're not, Repose is a CNJ's best friend, at least it is for me. You'd be surprised how much Repose/Sleep can help ease the burden on both you and the tank.
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Don't worry, I completed Haukke Manor as CNJ lv29 with 2 DRG and a LNC (we made the party while being distant to each other and realized the situation too late XD)
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I would only recommend waiting to go as job for tanks. I've noticed level 28-29 GLAs and MRDs struggling to keep hate off 31 DPSs. Once a DD has that Soul Crystal their stats take a huge leap and it effectively puts them several levels higher. Not only are they natively 2-3 levels higher than a 28 tank, but the +10 or so stat boost on their key stat puts them even higher.
But a 28-29 healer shouldn't have much trouble.