Personally I would consider anyone who voluntarily did a 5th year of high school strange, no offense. You haven’t been there long enough to realize this but you will outgrow high school long before you are done. AP courses are not equivalent to college courses; they are just massive, tedious, superficial surveys that represent hoops you have to jump through for competitive college applications. If scheduling conflicts prevent you from taking some, your guidance counselor should note that in his or her letter. And most rigorous courseload is a category, not a contest; it gets your application looked at, but it doesn’t get you in. Every year there are students who are shocked that taking 2 years of college level classes with A grades (I may exaggerate slightly, but you know what I mean) was not enough to get into an Ivy. I’m all for taking an extra year to do something interesting and different, like study abroad, but an extra year of high school at home sounds unpleasant, unnecessary, and likely to make admissions officers look at you funny. And also, if you take a gap year, do it for you, not your resume-- apply to college during senior year instead of ruining a gap year stressing about how to get your applications done.
You should focus on finding and developing your interests, not on building an attractive college resume. Paradoxically, that is much more likely to make you attractive to an Ivy than 4 years of carefully manicured classes and activities – provided you meet academic standards for admission. In any event, you should never set your heart on a reach school. Admissions to Ivies are a crapshoot-- you can be superbly qualified and not get in just because there are so many more superbly qualified students than there are spots in a class. And there are many, many schools that can give you an outstanding education and experience – it’s ridiculous to imagine that one school will somehow be better than all the rest, or even that you can make a rational evaluation of your dream school based on a few visits. I wish you luck, but I think you need to take a hard look at what you are doing.