OK, just because there is no hammer spur doesn't necessarily mean you have DAO. Whacking off the hammer spur was real popular at one time for various reasons. There was a factory DAO hammer, but I've never seen one. No idea what they look like or how they were different.
Try-with a verified unloaded gun-rolling the hammer back with the trigger until you can use your thumb on the top of the hammer to try and cock it. If the hammer cocks, it still has a single action notch. OK, that still doesn't solve your problem, but you at least have a clue as to what's going on internally. Conversion to actual DAO has been done by modifying the hammer or the trigger or both. If your gun cocks, you have a clue that the trigger is probably OK.
I've never read Kuhnhausen's book, but I don't believe I've ever read a gunsmithing manual that didn't have some bad information (I've got factory manuals with margin notes for changes). Some of which may have been due to either changes of methods/parts/standards or goofs that proof reading missed. Still, probably a decent guide for getting the side plate off and the parts in and out without buggering something up. American Handgunner may have videos on their website.
If sending it back to S&W isn't an option, you could try to find an armorer or smith that knows S&W revolvers and would let you look over his shoulder. Some might enjoy sharing the knowledge, others will view you as stealing their bread & butter. You could at least ask.
Numrich has hammers. If that's all you need, all you probably have to do is change out/install the primary double action sear & spring from the original hammer and install the hammer. That'll save you a lot of fitting. Make sure you test for push off.
DO get Brownells S&W screwdriver if you don't have it. Has all the tips (possibly except for the grip screw) you'll need to work on S&W revolvers.
You wouldn't think a revolver function and repair manual could be amusingly snarky...
