There was overwhelming support for reverting the Bladedancer to my original conception of a lightly-armored fighter, so I’ve done so. Below are the revised rules. As an executive summary, they trade down from platemail to leather in exchange for an initiative and AC bonus.
Bladedancers are skilled combatants. At first level, bladedancers hit an unarmored foe (AC 0) with an attack throw of 10+. They advance like clerics in attack throws and saving throws, by two points every four levels of experience. By religious doctrine, bladedancers are forbidden from debasing themselves with the fighting implements of the peasantry, or dishonorably firing missiles from a distance. A bladedancer may only use piercing and slashing melee weapons, such as daggers, swords, spears, and polearms. This eliminates weapons such as clubs, maces, and warhammers, as well as bows, slings, and crossbows. A bladedancer may dual wield a weapon in each hand, or fight with a two-handed weapon, but may not resort to shields. Bladedancers are only trained to fight in leather or lighter armor. However, they gain a +1 bonus to initiative and a +1 bonus to Armor Class if able to move freely. At level 7, the AC bonus increases to +2, and at level 13 the AC bonus increases to +3.
Let me know what you think. Also, should it stack with Swashbuckler proficiency? A bladedancer in leather armor with the Swashbuckler proficiency could have AC4 (2 leather + class bonus + swashbuckler bonus), comparable to chain, reaching AC6 (platemail) at level 7, and eventually at level 13 improving to AC8 (2 leather + 3 class bonus + 3 swashbuckler bonus), or better than non-magical plate.
Other ideas would be to trade heavier armor in favor of weapon finesse or skirmishing.