I just received my new 27" late-2013 iMac and the 32GB of memory I ordered from Crucial for an upgrade. I found the installation of the four boards to be much more difficult than installing the original Apple boards received in the computer. I don't know if they're slightly thicker or what, but I had to pull the whole assembly as straight up as I could and then work hard to wiggle and push the boards down far enough into the slots to make them connect. The first time I pushed them in, I got the warning tone on start-up that I had no RAM in the computer, so I reopened the back and wiggled/pushed them in even further. My message is: Don't give up, work hard to push them in, but be very careful you've got the boards positioned properly and don't force to the point of damage. Once I got them in correctly, everything worked fine.
I am sorry for your difficulty with installing them memory. I do appreciate the suggestions that you have posted I am happy that you were able to get the memory installed with persistence and patience. Have a wonderful day.