Obviously, it's not my place to try to tell you what to do, but it's pretty clear that you are going to have some really good choices when it's all said and done, so I wouldn't bother unless it's been your dream school since you decided to embark on this adventure.
The turmoil in the office really shouldn't be an issue for the typical applicant, but it caused them to put you aside (unless what is happening with you is their SOP and has nothing to do with lack of direction from the top), and thereby put you at somewhat of a disadvantage to applicants that were verified when you were and have already received IIs.
Personally, if I had 4 IIs in the middle of August, I would write off the one school that waited two months to send me a secondary rather than chase it. The only exception to this would be if you called them and they acknowledged that it was a mistake on their part, and you should have received it along with everyone else. Otherwise, given the delay, even if they ultimately clear you to receive a secondary, you'll have to explain and overcome a nothing IA that nobody else cared about, AND deal with whatever disadvantage stems from filing a secondary after IIs started going out. I'd put the $80 towards one of my interviews and move on.