WOW... this shows that I do not know the finer details on Dan's songs...I was first attracted to his artwork...and haven't followed lyrics/songs in detail like you...
I wonder now:
Perhaps he drew a pic of himself walking a cow (or envisioned himself doing so?), before writing Museum of Love, and of course - therefore - also before writing"Walking the Cow"?...and that image of him stuck with him? .... inside of his psyche...that he was walking a COW versus a dog? ...maybe because 'normal people' do not walk cows?...
and MAYBE? he even drew it before both songs, when he was feeling the feelings he later expressed in the interview? And, when he felt like a hick...and maybe not worth a second look/consideration by a woman like Laurie...or like his image of her?
...perhaps even the act of drawing it (or EVEN thinking it?) left a BIG impression inside of him, so much so that he needed 'to exorcize (sp?) it later, or just wanted to communicate about having those feelings?
I know it is all conjecture...and I hope you can get a bwetter rply, but I actually can see ALL of that as a potentially viable explanation, because I have a severely manic-depressive (and creative, but not at Dan's caliber) older sis, and I could FULLY imagine that fascinating (but sad to so-called normal people)
scenario happening with her...or someone like her...so, also with Dan- and, having met him, and knowing how my sister's psyche is...I can tell you, he (and she) is very aware of the 'burden of mental illness' ...the abnormality of it...
He did say that he is just a conduit when he draws...that it just flows...and, I saw him draw, at his parents' dining room table when he still lived with them....and that's certainly how it appeared to take place...
but, I feel - as probably most people would, I imagine - that it flows not only from 'Source,' but also from deep inside his psyche...and it is a catharsis or sorts for him...both to draw and compose...
Well... I also wonder, are you perhaps gathering info for the next film?

I ask because you are asking a great question...really addressing his psyche! Love it!
If so, that interview is certainly jam-packed...