Upgrade from HD560S to HD6XX? + Amp considerations

Hey Everyone - as the title suggests, I’m considering an upgrade path right now. I’ve been running my Sennheiser HD560S with a Fosi DS2 DAC/AMP dongle for a little over a year now as my first real pair of cans, and I’ve been very happy. As one does, I’ve gotten curious about something that might cater more to my listening preferences, which is how I’ve gotten to the question at hand.

First of all, I know for sure I need a dedicated amp of some kind for listening on my turntable. I’ve been looking at mostly Schiit amps, and my interest was piqued by their Valhalla 3 tube amp. And those I’ve heard are a perfect pairing for a HD650/6XX type headphone. I listen almost entirely to classic rock (Led Zeppelin, Pink Floyd, Fleetwood Mac, etc.), and to me, listening is an enjoyable (and often emotional) experience. The warmth and sound signature that comes from a HD6XX (especially when paired with a tube amp) seems to cater directly to that, certainly more so than my current setup. And perhaps I’m over indexing on it now the more I read, but I feel like I’ve been noticing more of the bright/fatiguing sound that the HD560S can be known to come with despite its technical accuracy.

I recently started playing with EQ settings, and I like the result, but I’m still left wondering HOW MUCH of a jump it’d be going from something like what I have now (or same cans + a less expensive solid state amp for vinyl) to an HD6XX running through a tube amp. Worst case I can always order both, give it a try, and return based on what I learn, but figured I’d ask here to see if anyone has any thoughts.

Thanks!