Your description supports your suspicion of an obstruction, but it is not readily apparent.
I suppose there is little harm in gently shaking or tapping the Mac (powered down, lid closed) in an effort to dislodge what may be a piece of debris that might be resting beneath one of the contacts, causing mechanical interference and preventing any possibility of electrical contact.
Shake and / or tap in various orientations. Maybe try using a vacuum, maybe try some compressed air, maybe a combination of those techniques.
Another advanced troubleshooting technique: have someone else look at the card that works vs. the ones that don't. Doesn't have to be a photographer or computer expert. Sometimes another set of eyeballs will notice something yours didn't.
If you don't get anywhere, physical disassembly will be required. Start here: Apple Repair.