It seems that I somehow managed to get it working on my Duo (v1) thanks to the tips above. The only thing was that I don't want my whole media share to be owned by nobody/nogroup. It didn't work with just a specific folder within the media share set to nobody/nogroup (permission denied error). So I had to create separate share dedicated for Transmission downloads, assign it to nobody/nogroup, give proper rights to this share, change setting for incomplete downloads in settings.json and it works fine for few hours now. Thank you guys!
Anyway, it would be nice in the further versions of Transmission to make it possible to set ownership matters somehow other way than just nobody/nogroup.