Here's what I got from local hardware store:
It's firm weatherstrip which just needs to be cut to correct length and put between the plastic ring and the padding. There's adhesive on one side to keep it in place but because it is firm enough it'll stay on just by itself.
And I can tell this mod makes a freaking world of difference to me in comfort as the ears are not touching bottom of the earcups anymore. However, firm strip makes padding harder on the stock pads, which brings slight discomfort factor of its own, so a bit softer strip would work better here. However, it can't be too soft otherwise it won't make any noticeable difference in space.
Here's the main culprit pressing against the ear:
And here's the mod with softer MDR-1R pads:
This is the most comfortable configuration I've found so far for these headphones. Now I just wish I've taken the black ones as it's much easier to find black parts for headphones.
Next I will probably test DT-250 velour pads, will see how that goes.