You're welcome!

"Kind of like trying to paint a room without all the prep work of taping it off."

That's a good analogy.

"In summary, do you count your way through a song at speed until you have it down and then do you find you have to think less about it and can just play it without having to think as much?"

I've been playing long enough that I usually only have to explicitly count out tricky subdivisions when I'm learning them.  For the most part I can count downbeats (quarter notes) through any tune.  The problem areas are usually matters of technical physical motions (complex parts of Bach pieces, for example), where the problem isn't so much knowing where and when the notes happen, the problem is getting my fingers to do it all in time!  So it's time to slow it down to get it exactly right.  Then gradually up to speed.

But yes, in general once I can do that I don't think about it consciously as much.  In fact the faster or more complex a part is you don't have time to think about each event.  You have to count on repetitious practice & second nature.  The goal is to think in larger units, to have practiced so much that a whole riff, phrase, or section is contained in your conscious mind as "that part", "that riff" & the hours of focused repetitious practice take care of executing the physical process.

First you practice until you get it right.  Then you practice until you can't play it wrong.

Make sense?