I'm ever so slightly ashamed to admit that it might have been a little brave of me to post about philosophy, since I don't know much about philosophy at all! I didn't know anything about Rudolph Steiner until I did a few minutes of intense Wikipedia research just now. Still seems pretty complicated to wrap my mind around; maybe I just need to try harder.
I don't mind speaking in public; I think it's kind of a rush, in a way. I like singing karaoke for the same reason. But it has to be something I'm at least moderately good at. Having been a teacher I've had a bit of practice talking to a crowd. Plus, it's not like anyone is going to harshly judge a eulogy.
Physicists are certainly mathematicians ("same thing as"--not really, but a category of mathematician). I suppose doctors have to be at least decent at math to get as far in their educations as they have to do their jobs. There's a difference between organized religion and spirituality, for sure, and maybe your venn diagram is an apt description. I suppose I would argue that spirituality, or any faith-based belief, is a kind of religion, but I welcome any disagreement on that point.
Regards the last point, you are definitely - regrettably - right on that front; which makes my research incredibly difficult. The Christians hate me (invariably when I tag my post as such) and the philosophers have me down as a Jesus freak. The New Agies have really bent "spirituality" as an innocent adjective out of shape. The associations with paganism and polytheism and feminism (let's toss that in amongst the goddesses as well) have made saying anything intelligent about the possible added value of spiritualising science near impossible. It takes a highly objective mind to see what can be done on that front and an ego that doesn't mind ending up with less belief in anything than when he started.
Hope you don't let eulogies go to your head for I'd hate for you to have too often an occasion to give one. Unless of course, you suddenly see the Light and become a priest, a rabbi, or an immam and give eulogies for a living. Teachers, preachers, the same difference really...