Yes, I am that guy. Shh! Don't tell anyone.
Anyhow, I realize that it is probably out of reach for you, which is why I quantified it. If, for example, you and five of your friends would all be going first class, it's pretty close to the same costs as charter. It doesn't reach parity until about that level.
It also helps if you aim for regionals, instead of the larger airports. That may sound counter-intuitive, but that's where I've had best luck organizing a flight. You can do spur of the moment things, but that starts getting obscenely priced.
It also really, really helps to have friends with planes.
And, again, I know it isn't necessarily something you can do on a regular basis but it really does make a difference. I only charter if I'm staying in North America. There is no way I can justify the expense for long international flights. If it is an international flight, I live right on the border and have Canadian citizenship so it's pretty easy for me to fly out of Canada instead.
As for the TSA, I just really don't like them. I don't mind customs and I understand the need for border security. I find the security theater to be offensive, however. I'd probably not mind if they actually were really increasing security. Israel has a good model, follow them. Either way, it is nice to completely skip them.
Back to the idea of regionals... The smaller airports are much nicer to deal with. I often use a small airport in Augusta, Maine. They can land a two-engine jet there and there's always someone willing to make a few dollars, even if just to get more flight hours.
Another one is just a little tiny grass airfield. There's a small private one in Rangeley and there is a municipal one in Phillips. Those are pretty good if you're not in a big rush. Best of all, you get to know the pilots and they will probably even let you help fly the plane.
At any rate, I like your idea of treating yourself to a chartered flight. Even if you're never able to do it on a regular basis, it is worth it just to enjoy the flight. I don't really like flying all that much, though I do enjoy being allowed to pilot the planes. You don't need a license to do so, as there is a pilot right beside you. It's actually pretty easy to not bump into stuff.
Then, of course, there is the experience of a more costly charter, where you even have a stewardess, food, and drink. That gets really costly but it's worth it as a special treat. My usual charter isn't much more than a plane and a pilot, I will even typically be loading my own baggage. That's quite a bit different than chartering a 747 with a full crew. Note, that's not something I have ever done. I have a few bucks, but I'd prefer to not waste it.
So, yeah, treat yourself to the luxury sometime. There are varied levels of charter. It really helps to get to know some pilots personally. They make great friends and are all very enthusiastic about flying. They will try to pressure you into buying your own plane and getting a license. They are a very passionate bunch.
As for the Über plane thing, I was surprised to learn that they have timeshares for planes. One of my local friends has a timeshare plane and that has come in handy. It's much less expensive to just chip in and take a vacation with him and his family. I can take the missus and we pick all decide on a destination. That is actually not that expensive. It isn't always the same plane, or anything like that. They have airplanes all over and the timeshare is just on the one you want at that location and that is equivalent to a certain class of airplane. (I can get better details, if you're really curious.)
Anyhow, sorry for rambling but I'm tired and there is a lot to say on the subject. I do highly recommend you follow through on your idea to treat yourself at least once. You can probably hit up your regional and fly to a nearby city for just a few hundred dollars. Charter isn't always complete luxury.