This is quite a coincidence, Peter.
I've been laboring with that same mystery since OS X came upon the scene, a "Save" (and stash) dialogue box that was much too attenuated over the "classic" one we all learned with in our first Mac(s). Somehow, I saw one, somewhere, recently, that was in the form of a "List View"– such as when one clicks on "Open" in a given application's menu. That was what I was looking for.
So, naturally, I went to kneel at the feet of Sir Pendragon, hoping he could provide me we guidance as to how to get out of the very fix you're reporting here . . . I think.
Somehow, while we were talking about preferences and such, I did something that – boom! – brought up the precise model of dialogue box I had been hoping to find. It's in there, by golly, and it's neat when you find it . . . after all this is a Mac.
I'm more than a little embarrassed to admit that I've been slogging along with the "wrong" display. As well as not being able to tell you I don't know how the transformation occurred. I'll be really interested to see if anyone can point out the solution. I haven't a clue
The principal reason I was looking for help on this matter is the fact that I've also decided – with the pending arrival of my new iMac – to discard a Documents partition, a really old "convention" that I thought I didn't wish to eliminate, since it was so hard to take a Saved document and, as you said, do anything with the "skinny" dialogue box but aim it "toward" the Desktop.
The List View version makes it really easy to put it in subfolder in the Documents Folder. Thank Goodness.