After about six months with the HF580, trying numerous mods and pads, I think that I finally started to figure this one out. The problem I had with all the mods was, that they were making the treble way too elevated sibilant and piercing. It was unbearable to listen to it for more than 30 minutes, when it became too fatiguing for my ears. I decided to remove all the mods, and start all over again.
After reading someone's post in this thread (sorry, don't remember who the credit goes to), I decided to find suitable pads first, and mod later, if I'm still not satisfied with the result. At first, I started modding the HF580 cause it was lacking the sub-bass that planars supposed to have. By pressing the cups against my ears, using stock pads, I managed to regain some of the bass I was lacking, meaning that creating a good seal between the ear and the driver is paramount for experiencing what this headphone has to offer. Because of the large cups, slim original pads and the low clamping force, I noticed that there is a gap under the ear that brakes the seal.
So, using thick pads, that confirm with contour of the area around the ears is a must. I guess this is why Sandy Aiva pads work so well. Since this discovery, I only used those
HM5 pads, and it sounds really good. I have numerous other HM5 pads that I'll try later and report, but from what I hear, I don't think there'll be much of an improvement, as long as there's a good seal. Maybe only if the pad is a whole and not perforated from the inside...