Just for clarification: 1) you did go through Settings, Device Info, SD Card, Unmount, then 2) opened SD card cover, pressed the edge of the card gently in to get it to eject itself for removal? In step 2 on your nc, the SD card did NOT eject when pressed? If this did not work and you have a B&N store within reasonable driving distance, then I would take it in before digging at it. If they mess it up, they can be responsible for any damage. Otherwise, you may just choose to file manage your SD card via the usb connection, assuming the card still works for storage. Anyone else have any ideas? Good luck!
You are correct, there is no "give" to the spring for the SD card mount. It's like it is stuck in there!
Having had 4 replacements for just this issue, I'm going to stick my neck out and say that it's a hardware defect that BN doesn't want to acknowledge. I'm guessing that the original designers thought most users will probably insert/eject a card a couple of times for general storage purposes like most smartphone cards, as opposed to camera cards that are frequently changed out, and didn't worry about the mechanism not being strong enough for frequent use. (I found this out within my first weeks of ownership because I was using 2GB and 4GB cards for movies, and changing the content outside the NC because the connections were faster.) I don't think BN ever considered the potential root users, especially those without dual boot options, who would be ejecting a card to boot back into stock.
My NC #5 has had the same issue since about the 4th or 5th insertion of a card, but I gave up on replacements because I got tired of redoing shelves.
You'll probably end up doing what I have done - get a set of fine tweezers and become used to very very very gently prying the card out only when you absolutely need to.