Right, so you agree that a proper "i love you" would ruin the scene. I think so, too. It's better without it.
I don't know what you mean by "proper" in this case. I think a big dramatized line would be melodramatic and sentimentalized, yes. But I don't think it has to be expressed that way to be proper.
He doesn't need to say it, Jack knew it anyway. Then if he is really saying it in such a rush that it seems almost comically, i think it's not making the scene better either, maybe even worse.
I don't think you and I are talking about quite the same thing. I don't think he's saying it out loud deliberately to inform Jack. And comically? I don't see much comedy in the scene.
Do you ever do things like, oh, you get out to your car and realize you left your keys in the house and you actually whisper/mutter "Oh, I need my keys" or something like that? (If you don't have a car or house, adjust the circumstances accordingly.) You're not telling it to anyone. You're not conveying information. You don't need to verbalize it aloud because the thought is already in your head and you're practically already turning back toward the house. But still, you say it.
Or maybe that's just me.
Anyway, that's kind of how I see this. Overcome with emotion, he actually forms the words. He's not making a declaration to an actual Jack he imagines is hovering there, anymore than he's doing that when he says "Jack, I swear ..." He's just saying it because he's expressing thoughts in the privacy of his own solitude.
Therefore, i choose to think he is just sobbing instead. 
OK!
