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He just sits in territory with a toughness of */0, protected from the discard. STS stays on him, because the convert never happened (and the "then" in the ability requires it to move to the next part, almost like a "to").
I would actually agree with redemptioncousin on this one. The reset to face value is an and with the convert, it's not dependent on the convert so I would think if the character is protected from conversion they would reset to face value and then begin decreasing again.
I was kidding. The play-as is definitely wrong in this case and I was kinda pointing that out.