I did finally get the problem resolved: it is now FIXED.
I received helped from Hikari on Android Authority forums. It turned out that I had a mild (but blocking) hardware problem. I removed the back of the Nexus 7 and pressed down on all connections, including a both ends of a metal "tape" that were peeling up from their contacts. After doing that I was able to once again get to the Recovery mode screen from the boot loader.