You could try the softer pad, but I doubt that would change anything and I believe the soft pad would likely result in some accidental rounding of edges and other undesirables. I don't know about others, but I found that, when I'm sanding something that is supposed to be flat in the end, the hardest pad available is the best choice.
Don't know why the DTS400 is a little more prone to vibrate when the piece being sanded isn't firmly supported, but the ETS125 seems to be more likely to do that for me also. I have always believed that it is a combination of the height of the sander and the fact that these sanders are vey light. When the pad is tipped just a tiny amount (not noticeable), then the sanders seem to vibrate. However, after using my ETS125 more, I found that I get much less of that, so it may just be getting used to the sander. Every sander (including those of other manufacturers) seems to have its own quirks.