My understanding is that most of his decline in net worth is due to problems with branding and security at his hotels / resorts -- i.e. problems with his non-publicly traded assets. In my mind, this would, if anything, create additional incentives for him to move public markets for his financial benefit to recover some of the money he's lost elsewhere.

Fair point, although the losses seem to be from the huge repetitional harm he's taken. He still may be trying to leverage the presidency to do what he can to improve his finances.