I'm not saying this is the case, I'm just trying to throw out some ideas and concepts. It's possible, since HD Speed is an AIO product, that it was filling some existing marring and that the ONR wash removed the "fillers". Again, I'm not saying that these are intentional fillers, just that it could happen. I have never used Speed and don't keep up too much with 3D/HD products, I'm just saying I've been at this a long time and all kinds of products can "fill", on purpose or not.
Also, if you are getting dirt on your drying towel, that's a bad sign. You want to remove the dirt with your wash media, even if it takes multiple passes. I'm not a great believer in flat sponges like a grout sponge or the BRS, I prefer the non-split microfiber wash media like "the bone", but typically I would use one side of the "sponge" on an area, then turn it over to the other side and re-wash the same area to make sure you've got all the dirt off the surface before you dry. As with any wash technique, the dirtier the vehicle, the smaller the area you want to do before cleaning your media.
I have to disagree with Ron that there will always be "some" dirt on the drying towel, you should strive to clean your sections thoroughly and overlap into the next section so you don't get your drying towel into the dirt from an unwashed section...what I mean is, if you are washing a door, you should wash an inch or two past the edges of the door, but only dry the door...that way you know you are drying a clean area.