I think you're definitely on the right track by comparing what you need to what similar subclasses grant, but ultimately your Sorcerer bloodline will have to compare to other Sorcerer bloodlines, first and foremost.
Also, I think Lil Mordecai had an excellent idea for UA Defense (10+Dex+Cha) rather than a permanent Mage Armor (or making it a bonus spell known, as I would have suggested).

The draconic bloodline gives: Draconic Language, 2x Prof in social interactions with dragons, UA Defense (13+Dex), and +1 HP per HD, all at first level.

I'd suggest giving your archetype (A) proficiency with light armor, shields, or simple weapons, (B) unarmored defense (10 + Dex + Cha), and (C) the ability to use a weapon or shield as a spellcasting focus.

At level 6, rather than the standard extra attack trait, perhaps consider the ability to cast a cantrip and make a melee attack in the same turn (I forget who can do that, bard or warlock probably) or casting a cantrip onto a weapon to add its damage to the next attack. Perhaps when doing so, you can add your Charisma to the attack & damage roll as well, though you'd want to limit the uses.