Thank you and also everybody else for the input!
Regarding brain burn in, I suspected that I would have to get used to the Arya and train my hearing, so did not expect to immediately get the full benefit of the better headphone, but I was still surprised not to be able to discern any difference. I feel a bit better now though after reading that differences should begin to become apparent relatively quickly. I will follow the advice to listen to the Arya exclusively for a few days, with only FLAC source material.
As for amps, I agree that I don't want the headphone to be held back by that, but I also don't really want to spend any more money right now. I did briefly look into used gear, but did not find really find anything that seemed like a good deal to me, but I will take another look.
Another possibility I am considering is getting the Sennheiser HD660S like I originally intended, which should work well with my DAC+AMP and still be a big improvement over the HD558, and maybe have another go at truly high-end gear in a couple of years when my listening ability is improved and my wallet a bit thicker. The general consensus of people who have heard both the Arya and the HD660S seems to be that they are similar in sound signature, with the Arya being better in every way, but not by that much. And the HD660S are only a quarter of the price...