Is there anything funky going on with the tonality?
It's not exactly stable. For sure. But what is it doing? That's all vanilla diatonic chords. But they're not functioning as diatonic chords... so they're pan-diatonic then. But so what about pan-shtuff. What's it doing with the tonality? Weakening it? Weakening it by pointing at another key? By pointing at several other keys? Is that what my ears are hearing? Is it 'vaguely pointing' at a few other keys at once? I'm thinking that's it. I think I could hear some of that, the upper part of the progression, as being in C, F, or Bb. But those are just my ears too. Maybe d minor too, when you start off in C Major -- I was thinking my ears may have want to keep that pattern going I iii V viio... then i III v VII. There may be something to that idea too. The form impacts how you hear the tonality.
That's what I'm leaning toward. I think the ears are always searching for a nice, comfy tonal center. Things can be heard in different ways. One note has many, many, many different colors based on its relationship to the tonal center and where it's going. Tonal center, chord it's in, function of that chord... Probably getting toward an infinite number of colors. Which is way music can sound so unique. That's my thinking anyway.
I suppose I should work on my ear training so I know what colors I'm hearing better. That would help, but I'm not doing that.
For this "progression" of whatever it is since it doesn't progress, group of chords.... For this group of chords I think the common chords between keys mean that my ears might want to hear those other keys. d minor to F Major... Might be C: ii IV or it might be F Major: vi I or it might be Bb Major: iii V. Or it might be d minor: i III. And something like voice leading, or just tapping one note a little louder than the rest, might affect what I hear as that tonal center. Or maybe my ears are confused... so the mind is confused too then.