Hey, I have some bad news. Quote from the FAQ:
Mithral armor: What exactly does it mean when it says mithral armor is counted as one category lighter for “other limitations?”
This means that mithral armor allows its wearer to use it when her own class features or special abilities demand her to wear lighter armor; in other words, the character wearing the armor is less limited. For example, a bard can cast spells in mithral breastplate without arcane spell failure, a barbarian can use her fast movement in mithral fullplate, a ranger can use his combat style in mithral fullplate, brawlers, swashbucklers, and gunslingers can keep their nimble bonus in mithral breastplate, rogues keep evasion in mithral breastplate, a brawler can flurry in mithral breastplate, characters without Endurance can sleep in mithral breastplate without becoming fatigued, and so on. It does not change the armor’s actual category, which means that you can still store a creature one size category larger in a hosteling mithral fullplate, and you can’t enhance a mithral breastplate with special abilities that require it to be light armor, like brawling (though you could enhance it with special abilities that require it to be medium armor), and so on.
Emphasis mine
=(
As for the Dragon Disciple PrC, claws wouldn't be the main reason one would go that route. The biggest benefit for a melee class is the bonuses to Str and Con, the Natural Armor and the energy resistance. Darkleaf leather armor would probably be the armor of choice because it doesn't have an Arcane Spell Failure chance.
For the Sorcerer level, using the Tatooed Sorcerer archetype would trade the unusable claws with a familiar.
Has anyone thought of using a Kasthsa as a race for the build? You would not need to a monk dip because of the multiweapon fighting feat, Perception class skill and +2 dodge AC.