The point is not that it is thematic but that there is a prize on offer. I would have tried:
16a. Usual two-letter initials for a prosecutor, five letter word for "up to" as in "what are you up to?", defn last 3 words.
28a. Defn is a lighting manufacturer, two-letter initials for a word meaning "huge" followed by a three-letter word for an old type of warship.