The hd560 feels like it lacks more cleanliness. It is clean, yes, more than others but I want more resolution in the audio. If the hd560s is 1080p I want at least a 2k (stupid analogy but you get my drift).
The imaging of the 560s is its weakest point, it's not very good.
I think if I were in your shoes, I'd consider giving one of the lower-cost planars a try, and maybe EQ the bass and treble more where you want it. Since I haven't used any planars, I'm not sure which is best, and which to recommend. But maybe one of the more recent/popular models by HiFiMan, like the Edition XS would be worth a look?
Comfort will probably be important with these, since they are a bit heavier and larger than dynamic headphones.
Resolve gives the XS some fairly high marks though for this, due to its swivelling cups, somewhat lighter weight (for a planar), and somewhat lower clamp.
The Edition XS appears to have a sensitivity of 92 dB/mW, which is on the lower side. Its impedance is only 18 ohms though. And both matter in terms of a headphone's drivability. It'll probably be a little easier to drive from a good desktop amp though, than a lower quality portable device.
The Senn HD560S looks a bit bright in some spots in the upper mids and low treble. And maybe a tad withdrawn in a few spots in the higher frequencies. The XS looks like it is sort of (but not exactly) the reverse of that. Maybe the HD 560S would not be a bad choice with a little EQ though, for a lower-cost open dynamic headphone. Some graphs of the 560S appeared to also have a slight imbalance in the upper mids though.
If you like a little more thump or authority in the bass, then maybe a good closed dynamic headphone would be also be worth a try?
Not sure what to recommend there.
On the lower end, most will probably point you to the K371. But I have a few issues with the design, ergonomics, and so forth on that unit. And am not as big a fan of its sound sig as some others are. There are also
some closed fans who like the Denons, but I haven't had an opportunity to try one. And they might also have a few issues with fit or sound sigs. The Denons (especially the more advanced models) are more than the K371 btw.
For lower-cost closed dynamics, I like my 250-ohm Beyer DT-770's fairly well. But they are dry sounding, and do need a fair bit of EQ-ing to even out their response, and to cut done some brightness. And are a bit harder to drive at 250 ohms. And they're not the most attractive lookin HPs
(though they are pretty comfy for the most part).
IAC, keep us posted posted on what you try, and how it works for you. I'll be curious to hear some more of your opinions on some of the recommendations and choices here.