After 4 hours on Apple Chat with several very understanding senior technicians, they came up with a plan for me to try. They wanted me to do a full, new, Time Machine backup and then shut down the iMac and do a COMMAND+R reboot and reinstall of El Capitan. Below you can follow what I did and the results. There is definitely some serious issues with El Capitan. The good news is that has been submitted to engineering at Apple and the have been made aware of this discussion. The bad news is that while mine did work better (found a way to not have to shut down the iMac to read an SD card), it still does not work correctly.
Status update:
I will try to do the best I can to explain what is going on after the COMMAND+R reinstall of El Capitan.
1. Did a full Time Machine backup
2. Shutdown PC, but did not unplug it from the wall
3. Put an SD card in the slot
4. Performed COMMAND+R reinstall of El Capitan
5. Waited for the process to complete
6. SD card was recognized on the desktop and functioned correctly
7. Ejected SD card using the software
8. Reinserted that SD card and it was NOT recognized.
9. I tried several more SD cards and none was able to be recognized
10. Did a RESTART
11. The SD card was recognized and worked (this did not require the PRAM reboot)
Now this is where it gets weird
12. REMOVED the SD card (not eject)
13. The warning tab did NOT pop up for improper ejection
14. INSERTED another SD card
15. Double clicked on the original SD card icon
16. Disc not ejected properly pops up
17. CLOSE the warning tab
18. Icon for the new SD card is NOW on the desktop
19. The new PHOTOS program takes over and starts loading photos for import without asking
20. Use the COMMAND+W to close PHOTOS program
21. SD card is ready to use
As long as I keep a card in the slot and do NOT eject it, I can change SD cards by just taking it out and inserting another SD card
But I always have to deal with the Disc not ejected properly process. So, for now, I keep a 256k SD card in the slot as a placeholder.
At least for now, I can function. But this software in El Capitan is not functioning correctly.