I found the answer myself, by chance:
Aligned Spellcaster, alternative class feature from Dragon 357, p88:
"Choose an alignment component you have that is not neutral. Spells you cast gain the appropriate alignment descriptor unless they already have the opposite alignment descriptor."
The only “Arcane Sigil Docent” I can find is from Dungeons & Dragons Online, and is not available in the tabletop game (that I can find, but I have read most of the Eberron books).
Usually a Warforged arcanist would take Unarmored Body, rather than Mithril Body, so as to avoid any Arcane Spell Failure at all. A 5% chance of even casting the spell correctly, on top of whatever chance you have of missing or the enemy resisting, is going to hurt a lot.
Note that if you want to be a bit cheesy (in some groups this would be fine, in others it’d be broken; depends on your group), Dragonborn from Races of the Dragon is an amazing template with Warforged, and would be perfect for a Sorcerer (who usually have some relation to dragons to begin with. Dragonborn replaces your racial features, but you retain any Subtypes you have. Since most of the best features of Warforged come from the Living Construct subtype, they keep all of those, losing primarily the composite plating and Slam attack. Since you want to get rid of (parts of) the composite plating anyway, this is a win-win.
The immediate answer to Arcane Spell Failure is usually the twilight armor enhancement (+1 equivalent), found in Player’s Handbook II and the Magic Item Compendium. It can be applied to Warforged composite armor, and reduces Arcane Spell Failure by 10%.
Other good answers, things like Thistledown (Races of the Wild), Feycraft (Dungeon Master’s Guide II), and Githcraft (Dungeon Master’s Guide II), all of which reduce Arcane Spell Failure by 5%, probably cannot reasonably be applied to Warforged composite armor. Even if they can, they’d almost definitely have to be part of the Warforged’s original construction (though a Githcraft Warforged would be awesome).
Again, note that with Unarmored Body or Dragonborn, you could wear a Feycraft-or-Githcraft Mithral Chain Shirt with Thistledown Padding, which has 0% Arcane Spell Failure before putting any magic on it. This is a great armor.
The Spellsword prestige class from Complete Warrior can allow you to ignore 10% of Arcane Spell Failure; combined with twilight, this reduces your Arcane Spell Failure to 0%. I strongly recommend against taking more than one level of Spellsword, however, since it loses a ton of spellcasting.
Best Answer
Okay. Let's go through the usual suspects and see how they can apply to your specific situation of 'reforging' existing armour.
This can be straight up added directly as a magical enchantment.
This requires the item to be mostly or entirely made out of metal, so either shadow silk or mithral, either way.
Having the armour reforged by a fey smith should actually meet the requirements of this DMGII armour template.
And ditto for the Gith. Going on a quest to have the Gith and Fey mastersmiths forge your armour into something worthy of a hero of legend will help get this into the game.
Can be worn under armour, no fuss, no muss.
Dragon mag, so ew, but doable.
Additionally, you could take the Spellsword Prestige class and reduce ASF by 10% a couple of times. There's a few other prestige classes that help you out, too, although none give as much casting progression as spellsword does. Your other major prestige class option is the Abjurant Champion which notably adds it's level to shield (and is often houseruled to work on mage armour too, since the writer mentions it in the description and clearly didn't realize it was conjuration not abjuration), which could give you a much higher AC than your mundane armour if so houseruled and even if not if you take the Arcane Preparation feat and prepare Luminous Armour (does not require exalted if prepared caster).