Which book/books are the most accurate/best concerning the M1 Carbine, specifically on maintenance, servicing, and identification of specific manufacturer parts?

I'm not sure what to tell you, there are alot of books, of which I have none.  But I do have a carbine.  I have an AGI video, which I like.  If you go to www.fulton-armory.com, they have books there.  If you go to www.surplusrifle.com they have books.  I think www.billricca.com has them too.  The surplus rifle site has a video of a guy breaking it down if that's what you're getting at.  The AGI goes much more in depth.  It's a great little rifle.  I love shooting mine.  I rebuilt my bolt and put a new recoil spring in and the thing runs real well.  It's not horribly accurate but not terrible either.  About a 4 moa rifle.  Maybe a hair more.  Some say this is bad some say this is good.  From what I can tell the carbine wasn't meant to be a tackdriver.

For the history and parts ID by manufacturer, "The War Baby" by Larry Ruth is about the best.
This is expensive, but it covers EVERY known marking part by part, and maker by maker.
It includes complete production histories of EACH maker.
It covers EVERY variation, every experimental, and every accessory.
This one gets into the FINE details.

Another is "A Collector's Guide to the M1 Garand and the M1 Carbine" by Bruce Canfield.

Also "The M1 Carbine Owner's Guide" by Larry Ruth.

The absolute BEST book on the mechanics of the Carbine is "The US .30 Caliber Gas Operated Carbines: A Shop Manual" by Jerry Kuhnhausen.
This covers EVERYTHING known about gunsmithing, repairing, and the mechanics of the Carbine.

You can get most of these from Brownell's or from Amazon.

The standard GI Ordnance manuals are also good for basic disassembly and repairs, but are nowhere near as good as the Kuhnhausen book.