Okay. Let's go through the usual suspects and see how they can apply to your specific situation of 'reforging' existing armour.
- Twilight, Magic Item Compendium and Player’s Handbook II, reduces Arcane Spell Failure by 10%. +1 equivalent, magic.
This can be straight up added directly as a magical enchantment.
- Mithral, SRD, reduces Arcane Spell Failure by 10% among other things. 1,000 gp for Light Armor or Shields, 9,000 gp for Heavy Armor, mundane.
This requires the item to be mostly or entirely made out of metal, so either shadow silk or mithral, either way.
- Feycraft, Dungeon Master’s Guide II, reduces Arcane Spell Failure by 5% among other things. 500 gp, mundane.
Having the armour reforged by a fey smith should actually meet the requirements of this DMGII armour template.
- Githcraft, Dungeon Master’s Guide II, reduces Arcane Spell Failure by 5% among other things. 600 gp, mundane.
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.
- Thistledown Padding, Races of the Wild, reduces Arcane Spell Failure by 5% among other things. 250 gp, mundane.
Can be worn under armour, no fuss, no muss.
- Caster Armor, Dragon Magazine #358, reduces Arcane Spell Failure by 5% 400gp Light/800gp Medium/1,000gp Heavy.
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).