I'm considering taking a level of Incarnate, and my race is Warforged, so it'd be good to know how chakra binds would deal with the fact that I'm permanently wearing armour everywhere. Magic of Incarnum pg. 51 specifies that I gain no benefit from magic armour, but I doubt a Warforged's natural body counts as magic. I don't want to lose the benefit of my Mithril Body feat, which is a +5 to AC, whenever I do a chakra bind...
Only the Soul Chakra comes into play, and that only at 19th
Warforged composite plating takes up the armor slot. Your other slots are free, either for items or for a chakra bind. Since it’s the armor slot, and soulmelds do not conflict with a slot unless you bind, that means the only possible issue is for binding to the soul chakra at 19th level or higher. As for that...
With a soulmeld bound to the soul chakra, it’s up to the DM
When you bind a soulmeld to a chakra, it usually fuses to your body in the location corresponding to that chakra. It prevents you from gaining any benefit from a magic item that occupies the corresponding body slot. (In many cases, it also prevents you from physically wearing such a magic item, as dictated by common sense and the description of the soulmeld in question.)
You definitely wouldn’t be able to benefit from any magic applied to your composite plating, but your DM very well may rule that any soulmeld you bind to your soul chakra fits comfortably over your plating: after all, the composite plating is your skin, and fits snugly against you. Mithral Body is not magic, so a favorable ruling about composite plating should remain favorable even with Mithral Body.
If your DM doesn’t let you...
The Unarmored Body feat could have fixed this issue, but it would mean that from 1st to 19th, you’d get neither the composite plating nor the soul chakra bind. This isn’t really bad (you can buy better armor than the composite plating, which is pretty awful), but it is an annoying feat tax. Anyway, it’s 1st-level only so that doesn’t help your existing character, plus it’s incompatible with the Mithral Body feat you want to retain.
(You could also cheese around your composite plating by undergoing the Ritual of Rebirth to become a dragonborn of Bahamut. This eliminates most of your racial features—including the composite plating—but one of the things it leaves is your subtypes. 90% of warforged features are actually features of the living construct subtype. This is an obvious corner case—living subtype provides weaker versions of construct features, but since it gives you those features instead of removing features from the construct type, you keep them when you become a dragonborn and lose the construct type. Absurdly, even though one of the few things you lose is composite plating, due to its precise wording, Mithral Body is unaffected, so you could even have your cake and eat it too.)
The other solution is the Split Chakra feat, which you could take at 18th level in preparation for your soul chakra opening up at 19th (nothing in the feat says you have to choose a chakra you already have open). That saves you a feat for 17 levels, plus, ya know, it’s something you could choose to do with your existing character who didn’t take Unarmored Body at 1st. But it means you lose an 18th-level feat which may be quite valuable.
The other other solution is just to multiclass and not pick up the soul chakra at all. Yeah, it’s kind of a capstone, and several of the options are pretty sweet, plus wow is perfect meldshaper awesome, but there are some pretty nifty incarnum prestige classes, plus incarnum mixes well with other classes. You’ve already taken a level of swordsage, for example: take another and get Wis-to-AC. Or take a dip in cleric; it’s super-fitting for incarnates and is the most powerful single level you can take. Could head towards sapphire hierarch after that one, too, though you better find some +Wis items pronto if you do.