That's a lot of dirt on that white pad - You're just grinding that dirt into the paint. I would consider claying next time after a wash, and being meticulous about getting the paint clean before using any AIO or polish. I doubt the swirls you're putting into the paint will come out, even with HD Speed, and definitely not with Klasse, as it was pointed out that it won't have any correction abilities.
I'm in the HD Speed camp, too - It's just so easy to use. Even though the members here pointed out that Klasse is in fact, available and affordable, I'm of the opinion you get more for less with HD Speed. I haven't tried HD Poxy over Speed yet, however I've been putting BlackLight over Speed, and been quite happy with the outcome.
You mentioned that the Klasse was lasting a long time for you compared to others, which is fair - However, I would probably recommend a fine cut cleaner before it though. Maybe M205.
What type and color car is this on? Any pics?