Hmm. I don't go delving into this stuff, but this doesn't seem very likely to me.
The main place I've seen Harry and Andrew linked is on here by people who are generally saying "see Harry isn't as bad as his uncle". And honestly I can't see the palace trying to link them together as spin. The palace would want negative stories to disappear as quietly as possible and putting Harry and Andrew together gives a delicious piece of gossip that would last far longer - plus they'll know how Harry can't resist answering back, which continues the story and bigs it up.
I suspect what they'd really like most for both of them is that they fade into obscurity with occasional notes at the back of the paper "Harry, formally known as Prince Harry walked to the end of his drive to collect the post last Wednesday".
Yes, people might see Harry as better than Andrew, but not that much. I don't particularly go out of my way to read articles, but I do follow the comments and they are overwhelmingly far more negative than anything ever put here. Yes, people will only comment if it means something to them so you tend to get polarising views, but even a year ago there were more "well, he is the King's son and the Kind should welcome him back" comments.
I'm not sure what blinder he's meant to have played over his security. As far as I can tell he issued one statement implying he was definitely getting it back, and another that if he didn't get it back then it was all the palace's fault, neither of which seems to me to be anything that would count as even a little bit positive.
The judges are professional people who will ignore little things like a prince having a strop. If he thinks that sort of thing influences them, then it's a bit like when you say no to ice cream for breakfast to your toddler and they throw themselves on the floor and scream. No (sensible) parent has ever said "oh I see how much it matters to you, I'll get the ice cream".