We're all dealing in the world of opinions here, but IMHO, if price is not a defining factor (and based only on the recordings I've heard, etc. etc. etc.) if I were you, and having a decent-size budget of $1500, I would maybe skip the CA-11. I don't find the cardiods to have the richness, especially in bass response I personally like in a recording. I stress that *many* other people will beg to differ, and at their price, I agree they are the best mic money can buy.
I've heard some awesome recordings with the only-slightly-more expensive CA-14 and think they're a much better choice in Church gear. Also, Chris makes some cables that can be used with Audix 1280 capsules (available in omni/cardiod/hyper) that cost somewhat more, but offer really nice performance (I've only used the cards).
If you're really focused only on using an low-profile omni mic, and again, you are willing to spend $1500 or less, I don't think you can do much better than the DPA 4060 (or the less sensitive 4061, though for jazz the 4060 should be fine). They are much smaller even than the Church mics, and I think they sound pretty amazing. A new set can be had for $1000; a used set for several hundred less.