At last I found a traveling case for my HM-801: a Nintendo DSi "Comact Case" made by Hori.
It is semi-soft with pleather outer cover and some kind of wowen felt or whatever on the inside.
Both the player, a set of IEMs and three SD-cards will fit nicely in it. If you have the Balanced Amp card mounted the player will still fit in there since the case is flexible.
The three pockets are made for game cards for the Nintendo, but are simply perfect for SD cards. There is also a pocket for the DSi stylus, but at the moment I have no use for that pocket.
Hope this is of use for those still looking for a case for their HM-801.
I have removed the brand tag on the border of the case (see first photo)