Andrew, to answer your question ... I'll just focus on the ProPhotoRGB to sRGB pair ...
For softproofing, I used a "Customize Proof Condition" using "sRGB IE61966-2.1" as the "Device to Simulate" with "Preserve RGB Numbers" checked ON. I am not given the option to choose a Rendering Intent, Black Point Compensation, nor Display Options (i.e., "Simulate Paper Color" & "Simulate Black Ink").
For profile conversion, I used "sRGB IE61966-2.1" as the "Destination Space" with the Adobe (ACE) Engine and a Perceptual Intent (with "Black Point Compensation" & "Use Dither" checked ON).
OK, after checking all of this, I went back and set up a new custom proofing condition using "Preserve RGB Numbers" checked OFF. Now I'm given the Rendering Intent and Black Point Compensation options. Now I get the same results as for the profile conversion. So it was pilot error -- I didn't realize that I had checked "preserve RGB numbers". Why would anyone want to check this on anyway?
Thanks for forcing me to carefully check what I had done!
Rick