AFAIK, there's no HDEO that's rated for it's cleaning ability of past deposits. These oil typically by design, have increased abilities in hold particles in suspension (like soot when used in diesels), as compared to PCMO's, but even then they aren't comparitively rated.
FWIW, I have read something recently around here or perhaps in my fumbling around on the web, that mentioned HDEO's do have a detergent-like effect, however weak in comparison to what one might think for a "soap". Wish I could remember where so I could give a link.
As for the low ZDDP thing, I really wonder just how real the problem IS as far as side effects of it use in today's cars - perhaps the engines are more likely to consume oil and/or cat.'s and other exhaust sampling devices, but could they also be made less robust than before and thus fouling sooner? That's what one gets when making demands (car manufacturers), without giving factual reason(s)...more questions and speculations!
Off my soap box now.
Good luck.