**edit** - Glad you thought it made sense, here is with a little more thought put into the abilities.
I think having significant amounts of healing coming from a Tank for the party would be impossible to balance. We already have a supposed "drain tank" and it's already incredibly hard to impossible to balance.
I also think that the job/relic weapons should be fans, or something in that vein, rather than fist weapons. but that would just be graphical and not really have much of an impact.
I think this would work well but IMO you would need some modifications. I think the Dancer should rely on Steps (which would basically be the Dancer version of Attacks) and Dances (which would basically be the dancer version of songs from the BRD).
I think leaving Greased Lightning in place is important. Because every Job still has to play like the class. I.E. a Bard is an Archer with songs, so a Dancer should probably be a pugilist with dances. GL may have to be rebalanced though. I propose giving you 5% evasion per stack of GL, which would be a good chunk of mitigation against direct attacks once it built up.
But would it be too DPS'y to leave the Dancer with 21% damage and 15% attack speed? A Dancer tank would already lose a significant portion of damage compared to a monk. They would lose 5% from Fists of Fire. They would lose 11% from Dragon Kick (though they would benefit greatly if a monk was dpsing). They would lose 40 potency on Snap Punch and 40 Potency on Twin Snakes, and 5% crit chance on True Strike. The Snap Punch and Twin Snakes would be the biggest factors, being, respectively a 29% and a 23% drop. This would leave a Dancer's "primary" rotation at ~370 potency before buffs, and 485 after, or about 81 Potency per second assuming~2 second gcd with greased lightning (89 with a monk dps). Compared to a monk doing a lazy flank rotation at ~146 potency per second assuming the same GCD. That leaves the Dancer at ~1/2 of the damage a monk does in a lazy rotation, though it could close the gap slightly with dots, I think that's pretty good and in line with the other tank vs. dps in the game currently.
Keep in mind a Dancer Tank would be more reliant on their DPS as they wouldn't have the big enmity combos that the other dps have. On the other hand we traditionally have skills nerf the tank damage when they increase enmity. That may not be necessary here.
Level 30 - You're right this basically has to be a "super defiance." Since PGL has no big enmity skills this would have to be a huge boost to enmity over normal PGL skills. I think it would work best as either a second buff to compliment Fists of Earth, or a "fists of ____" perhaps Fists of Light. If you left it as a corrolary to Defiance/ Shield oath, though, you could run Fists of Earth which would help with the EHP you need to be an (Evasion) tank, which would be important. I could see it being something like:
Fan Dance - Increases Enmity Generated (and potentially reduces damage dealt). While under the effect of Fan Dance, Each stack of Greased Lightning grants 5% evasion.
Alternatively, we could have another fist skill akin to how monks get Fists of Fire. I could see it something like:
Level 35 - 10% damage redux from fist of earth still isn't enough EHP to survive, so instead of Drain Samba being a life-steal/group heal, have it be a debuff and in the rotation, something like. This would leave the other buffs intact which, I think, would be necessary to maintain a decent amount of enmity, as getting those GL stacks would be critical to generating enough enmity via Drain Step.
Drain Step - ~120 potency attack, Generates a high amount of enmity (probably the same multiplier that Butcher's Block and Rage of Halone have), Oppo-Oppo form bonus - reduces the target's damage by 8%.
This would essentially replace Bootshine in the rotation.
Level 40 - PGL is lacking defensive cooldowns. Assuming the off class was PLD the PGL would have 2 bonus incoming healing cooldowns, but would need some survivability particularly against aoe things that are undodgeable. So how about:
Divine Waltz Something like: Reduces aoe damage taken by 30%. Costs X mp / sec (like the bard songs.)
This might be overpowered, so perhaps 20% or a higher mana cost wold be required. Ideally you could only maintain it for about 20ish seconds and it would take ~90-100 seconds to refill the mp pool.
Level 45 Still a Dancer would lack enmity, having only the step and the bonus, so perhaps something like Flourish could either be an AOE taunt (boring) or something more interesting like:
Flourish - Reduces the Enmity generation of all other party members by 50%. Duration: 10 seconds. Cooldown: 90 seconds.
This, I think, would be an interesting and unique mechanic. Unfortunately it wouldn't really be a method of AOE tanking. But perhaps this + Flash + Arm of the Destroyer spam would work. I still worry that aoe enmity would be a problem.
Level 50 - I like the trance idea. Dancer would need TP management badly and that seems like it would be the only thing that could work, essentially reduce the cost of all attacks to 0 though, not just dances / steps. Of course this would only really be required if the Dancer didn't have access to Lancer skills, and honestly Lancer might be the best option as a tertiary skills source for the job. If it was this would need to be something else. As it stands I'm not sure if it's an amazing lvl 50 ability but it seems good to me.
Trance - Reduces the TP cost of all abilities to 0. Duration 10 seconds. Cooldown 120 seconds.
I see a few other problems. First, a dancer doesn't have a high armor value like the current tanks, so I'm not sure if 10% reduction form Fists of Earth, 15% bonus evasion, and 8% reduced damage from our step would work out to enough mitigation.
Another problem might be armor stats. Dancer gear wouldn't have much parry rating which is really the only tank stat in the game right now. and I don't know if the accessories alone would be enough parry rating to matter (i.e. hit the breakpoints). Perhaps reworking one of the skills would be better, or adding something to the Tank Stance which would swap your parry rating with crit rating (though this would make choosing accessories difficult and annoying, perhaps adding 25% of your crit rating to your parry rating would work better).
Anyhow I think this would be a really neat character in concept and execution.