But now I'm convinced that it must be about a dog.

Listening to the words again, I kept wracking my brain for who--or what--qualifies for the description, and my best guess was a dog. That's all, no dog in particular, although maybe they had one in mind.

Who would lay down across a body of troubled water like a bridge? Your best friend, a dog.

and yours is a poignant interpretation.

Now I'm going to wake my dog up and hug him.

S&G were/are one of my go-tos since the 70s. The Boxer is another good one.

I lost my best bud last October and still have not recovered. Hug your's extra for me.

And your interpretation certainly works.

Paul McCartney wrote Martha my dear about his dog, so why not.

That said, Paul Simon has said it was about his wife.

Popular lyricists often make their lyrics broad enough to appeal to multiple interpretations, it helps either popularity and also makes a song more interesting.

I watched two guys fight over this original and Aretha’s cover.
The stupidity of that moment over this beautiful song never left me.
Both versions are fabulous.