I won't advise you, but I'll tell you what I think I'd do. I'd apply anyway. And if I had the opportunity to interview, or give any feedback, I'd speak boldly. I'd own my mistakes, and explain that I was the type of person that owned my mistakes, was accountable for them, made them right, and learned from them. That I wanted what was best for the department and felt that my many years of experience and success made me best suited for this position and couldn't be erased by one lapse of judgment that I had learned from. That if they are looking for who's best for the department I felt that was me due to what I bring, and unless they have a candidate that has never made a mistake I want full consideration.
All in all, I wouldn't be deterred and would press hard until they told me no officially.
I think you'd learn a lot from doing that. It may be that the big boss doesn't 'forget', but that they make their decision based on the overall picture and this isn't as pivotal as your manager thinks. It may be that they are impressed with you stepping up and asking for what you want and telling them where you want to be. Even if you don't get this position, they may see where you are aiming and start considering you in this light and giving you guidance or career planning on how you could make that happen. All good stuff.
And, if for some reason this person is petty and forms lifelong opinions based on superficial data...well, might as well find that out now. You can continue to do your job and put feelers out to other companies that might appreciate your experience. But better to find out now than waiting 5 years and hoping they suddenly have a change of heart.
In the end I've never let someone I didn't like control my career. If your boss's boss is a jerk, all the more reason to apply (both here and elsewhere). If I don't like someone why would I give them power to make me pass on pursuing where I want to be? They're going to have to shut me down publicly, I'm not going to cower in the back and wait for them to invite me into the club.
OK, that's just for me. Honestly I don't apply for many jobs. For the most part I just try to kick enough a$$ where I'm at that I get recruited somewhere. But I've had a couple of boss's that were so bad I walked out without something else lined up. Bottom line, either I want to work somewhere where I can just excel and trust them to reward me, or I want to go somewhere they do. I don't want to have to fight for what I deserve. It's enough of a fight to do a great job, no reason to do that and then beg for scraps.
Either way I trust you and know it will work out. Total confidence is what I have in you G.
Me:38 XW:38 T:11 years M:8 years Kids: S14, D11, D7 BD/Move out day: 6/17/14, D final Dec 15