Regarding tidal locking....?

Interesting question. If the Moon has a "heavy " side, then as the Moon's rotation slowed to match its revolution rate, it does seem as though the "heavy" side would represent an equilibrium point that would result in some form of harmonic response before it damped out.

As far as the momentum, I suspect most of the losses were indeed just losses (viscous / friction) resulting from the movement of the tides on Earth. It is not an isentropic system. If there was a compensating gain in angular momentum, it may have been a slight increase in the orbital radius of the Moon - thereby increasing the moment of inertia. But I sort of doubt it. I suspect if you count all the losses due to tidal motion, that it's really fairly substantial. I think this would balance the equations.

It still does that, a little bit. It's called libration. This shows it nicely:

http://en.wikipedia.org/wiki/Libration

And I'm sure it was much more extreme in the past. Here, imagine this: the first day when it didn't make it all the way around. It just slowed down and slowed down and then, right at the 1/2 way point, started coming back.

As for your conservation question, I'm not sure, but I'll bet it's the tides as well as the slowing of the earth's rotation.

As Larry said, there is a heavy side to the moon. It's quite eccentric by mass, so this would no doubt have the effect of speeding up this synchronization. I didn't mention it, though, because I was unsure of how long that eccentricity might have been in the making. IOW, how much is it a cause and how much is it an effect?