I came to this thread late, but ...
For me, this subject has been a "Grail" type search.
IMO, when selecting "wash media," my focus is on where are the dirt particles going as I'm cleaning the surface. I want the WM to take up some of the particles and not just drag it or spread it along the paint surface, and that's why the Schmitt makes me uneasy. Whether I'm using a grout sponge or a MF mitt/towel, I'm going to be moving it across a grit guard to get out as many particles as I can before reapplying.
Grout sponges seem to work fine for me, but at the moment, I'm partial to (and just more comfortable with) thick MF mitts and/or towels. What I like about using ONR is that yes, the MF does get blackened with dirt, and some of it you can't rinse out, but this lets me know when I need to change MF's.
As for wheels, I am currently spraying on some P21s wheel cleaner or an APC, then brush off using my ONR solution, sometimes spraying a little H2O or ONR solution with a bug sprayer (which I just broke

) to get off excess cleaner.

I do one wheel at a time and it works fine.