So, Magic of Incarnum page 195 has the Soulfused Construct template. It can be applied to any construct without the Living Construct subtype, or an intelligence score. It gets some minor boosts, such as the Living Construct subtype, Essentia equal to 1 + 1/6 levels, the ability to invest essentia like a Cloak of Resistance, +2 dex and +4 cha, Int is set to 3, and Con is set to 10. Here's the fun part: under the Hit Dice column, it says to see the Advancing a Soulspark section on page 198.
A soulspark not created by means of the soulspark familiar soulmeld gains 1 additional point of essentia to invest in its incarnum shroud for each Hit Die it gains. Its Dexterity and Charisma scores each increase by 1 for every 4 additional Hit Dice
Bolding mine.
So while the first half of the ability is largely useless (you don't have an incarnum shroud, after all), the second half could be interesting as it's an unnamed bonus type. While Soulsparks are of the outsider type, and not constructs and therefor ineligible to gain the Soulfused Construct template, it might be arguable that the incarnum shroud restriction is irrelevant since you never have that racial feature.
So how hard would this be to shove onto a creature? Warforged Incarnate Construct Dustform Soulfused Construct looks like the easiest and quickest method, to me, netting a total LA of +1, but not a whole lot of good abilities. You basically lose your composite plating, and that's really it, unless I'm missing something, and gain some minor stat boosts at the cost of your Int going down to 3. Is there a more elegant method to get this onto something without tanking Int?