First, I think you do very well in capturing that sort of giddy excitement in having a belief undermined and the world turned upside down. I find it a rather addictive experience.
"It will touch each and every idea, and change it, and move on."
Sometimes I am having a conversation and I say something like 'we should stop dumping garbage.' There are ways that I can believe this validly. I could mean that we should start a better recycling program. We should change the sort of consumer goods are available. We should make people more conscious of what sort of place they are creating. But I don't know any of these arguments because this belief comes from the time before I learned to analyse and challenge beliefs, before I learned that I could fight back if a belief is challenged. Before I learned that I can see my belief in even the material world temporarily vanish without breaking. (It came back, which is nice because I like the material world.)
So there are residual beliefs, unless you systematically change all your beliefs at once only some will be changed. It is possible to have obsolete beliefs, which is really weird.
The philosophers I study under criticise the sciences for not being rigorous enough. The problem goes both ways. The sciences often do not understand the basic concepts from which they are functioning. A good scientist will also have a rudimentary understanding of philosophy, in order to fiddle with the background epistemology of their work.
You are correct in thinking that Continental philosophy is not continuous with the sciences, because it is the core of the humanities and as such being continuous with the sciences would be unnatural for it. I still think that asking questions about our connection to existence is interesting and important, although I personally do not find Continental philosophy as potentially fruitful as Analytic.
Intuitions are by no means accepted within the discipline as a whole, and are also an interesting topic of debate within it. Because philosophy is a highly speculative discipline it isn't going to be following a normal scientific model, but instead will model constant discovery. If you want to see where science connects up with philosophy what you should look at is the disciplines that end up coming out of philosophy as questions that can be answered scientifically. This is what we produce with regard to science.
Philosophy is the core of the academic disciplines. It isn't in the business of scientific inquiry and it should not be. Some philosophers are still looking for universal truths after all. Simply disagreeing with the idea of a priori does not make it go away.
It is good that you recognise there are problems in philosophy. Too many people take it as dogma and do not question the area they have explored. My advice is to take what you can from the discipline well keeping in mind that every piece you take comes with a centuries long dialogue.
I looked up rejection therapy. It has a strong similarity to Stoicism, except that Stoicism requires not being attached to outcomes both in the social context and when interacting with inanimate objects. My confusion is with the implications of Rejection therapy. In Stoicism you do not become distressed because it is according to your nature as a human being to aim at certain things (friends, a warm house, a cow.). Aiming at those things in accordance with your nature is virtuous. Acquiring these things does not make you more or less virtuous. But with rejection therapy real rewards are offered which will not necessarily appear to those who have learned to deal with rejection.
I'm curious about this program. My main concern would be the dogmatic aspect, which I suppose is present in every 'boot camp' style program. I think that the strength of a university program over this sort of program is that university teaches you independent thinking whereas this could lead to dependence in those who did not have a strong sense of individuality. The difficulty would be accommodating those people.
This is the first Less Wrong post which I have read and really deeply agreed with. I haven't done much teaching, but I am used to teaching those who I am on equal footing with, my fellow students. Teaching people who don't have background knowledge, who might not feel comfortable saying 'I don't understand' is really hard.
From my inept experience learning to dance I can say it makes it much easier when the teacher recognises that it is hard for you, although easy for them. That little piece of recognition, even without the ability to modify your teaching style, makes learning easier.
I have also had the experience you relate, but from the opposite side. I volunteer as a peer counselor. From time to time our training involves practicing with other volunteers. One of us pretends to be the client and we practice our skills. I love doing it and I had no idea that half the volunteers hate it.
I wouldn't actually link it to introversion/extroversion. I am shy, especially in groups where I am unfamiliar with the appropriate way to behave. Even when I feel like I am participating often I find that I am not, such as in seminars. I need to know most of the people in order to speak. But if I'm given a role to play that goes away. As soon as I know how to make sense of my role in the group I can interact. That's why I love simulation, because I don't have to be me. I can pretend to be a certain kind of person, the kind of person who would be function well in this situation.
I would say playing is the best thing you can do. Play with ideas, ways of behaving, etc. Improvise. Join a free style dance like swing without a regimented set of moves.