Okay: Incarnate Construct Tauric Effigy Soulfused Construct Warforged+Whatever animal.
Ending La, +2. Incarnate Construct -2, Tauric (per mm2 update. Humanoid LA +3) +3, Effigy None (Actually a null, but it's due to not having an int score, which the next template negates), Soulfused +1. End result, +2.
Total changes/losses:
Types/Subtypes: Lose Construct type, gain Humanoid type (incarnate), Lose Living Construct Subtype, become Monstrous Humanoid (tauric), Lose Monstrous Humanoid type, gain Construct type (Effigy), gain Living Construct subtype (Soulfused) - End result: Construct (Living Construct).
Scores: Str (Base Animal/Vermind/Whatever used for lower half of Tauric) + 4, Dex Base bottom Half, Con 10, Int set to 3, Wis set to 11, Cha set to 3. That's kind of kicked-in-the-face on the mentals.
Special Attacks and Special Qualities: Retain all natural attacks from bottom half's form, lose and then regain warforged's slam attack, retain all special attacks of lower half EXCEPT those with save DCs based on Con, Lose all special Qualities of lower half, gain some crappy x/adamantine DR, get free essentia equal to 1/6th level, soulbound resistance ability, and possibly 1 essentia/level for free (depending on how that ability listed under Hit Dice for soulfused is read).
Conversely, this could all be done via Animated Object + Soulfused Construct, or even just Awaken Construct. So really not worth it.
That's about what I give up with for trying to utilize this in some weird fashion. Not enough gain for the effort, and it's easier to do other ways. Awakening via Awaken Construct, despite being a 9th level spell, would be the easiest way to do it despite having to extrapolate an LA for it, no matter what. I am disheartened, now.