MP3tag is a tagging program but no graphics editor.
Even adjusting the cover size has only been added a very short time ago.
To get progressive jpegs into the baseline format there is a thread with some hints:
I do not think that there is really a way around an external treatment.
BTW: I think it is a poor implementation on Sony's side to forget the perfectly valid progressive format. So your initiative could just as well go to Sony and ask them if they could update their software on the players.
(I know: they won't.)