I think that's a cool way to see it! I interpreted the first verse as a few different scenes instead, mostly cause of the "she said, 'I'm sad', somehow without any words" part.
"short steps, deep breath. Everything is alright"
-I agree that this is definitely John when he's trying to work up the courage to ask River out. Like, how he gets pushed into River's view by Nicholas; one would probably stagger a bit as they are being pushed
hence short steps.
He also literally takes a deep breath trying to calm himself down, and right before that, Nick says "everything's alright".
(it's interesting to note that this is actually in reverse order, like how the memory traversal works. may just be a coincidence though)
"chin up, I can't step into the spotlight"
Well, a spotlight is something one would be in if they were, say, talented or had something special about them that they wanted to share with the world. But Johnny didn't feel special, he felt like he was a typical person who didn't stand out at all. So maybe he can't step into the spotlight because he feels like he's not qualified to do it, or he's not allowed to(aka he literally can't). That would have more to do with his brother, I think.
"she said, 'I'm sad.' Somehow without any words,"
(if you change the punctuation it either means that she expressed sadness without saying anything, or that she did say she was sad, and then John couldn't find the words to reply, tying into the next lines)
I think this likely refers to when River started folding the paper rabbits; John said, "You're acting strange, River. Is something wrong?" To which "I'm sad" might actually be a legitimate answer, but she didn't say anything and just looked upset.
"I just stood there, searching for an answer..."
This could either be when River keeps asking him to describe the rabbits, and he can't come up with a good answer to give, or when he's standing over her grave, wondering why she gave up her life for the house and Anya (he did mention that he didn't understand).
The second verse is a bit more general, I'm with ya there.
"Why do my words always lose their meaning?"
River's words are often not understood by Johnny, but not necessarily just because of her. For example, he didn't get why she kept folding rabbits, and why she asked him to throw the hacky sack towards Anya. It meant a lot to her, but nothing to him because he forgot. She might have also thought that their conversation as children lost its meaning to John and wasn't important to him anymore - losing meaning over time.
"What I feel, what I say; there's such a rift between them."
Pretty self-explanatory; she can't find the words to express herself properly, or she can't bring herself to say them. She probably felt very confused and betrayed when she realized John didn't remember their first meeting, but all she could do was ask him, "What else?" which actually sounds kind of desperate in and of itself...
"He said, 'I can't really seem to read you.'"
This happened a lot throughout their lives, so I'll just leave it at that. One moment was when she almost fell off the cliff going after the hacky sack and John asks if she is crazy. She didn't think he would actually throw it, possibly. He had no idea it was important though, since he forgot and she never said that it mattered to her.
"I just stood there. Never know what I should do."
I feel like the importance of this may be more like highlighting that River and John are actually quite similar in relation to each other. They didn't realize it, but they probably felt the same way when it came to communicating with each other.
What about the chorus; any interpretations?
