Thanks for your thoughtful reply. I decided to give it one more try keeping in mind what you suggested. I was able to get it to work only after doing the following:
1. De-select scanner sharing on the Mac Pro. The scanner is attached to the iMac via USB2.0.
2. Drastically shorten the computer name for each computer. The original names were so long that they aroused my suspicion that they were too long.
3. Use the Image Capture application from Apple (There is a scanning feature in Adobe Acrobat Pro that works very well when the scanner is connected directly to my Mac Pro, but it apparently doesn't work on the Mac Pro when the scanner is attached to the iMac and shared with the Mac Pro. This gave me some misleading connection failures until I decided to use Image Capture.).
4. Discontinued trying to use the Epson Scan software that came with the scanner. Apparently, Epson has changed its approach and no longer provides scanning software. Instead, they provide a TWAIN compatible driver that enables TWAIN compatible software to run the scanner. I downloaded the new driver to both the Mac Pro and the iMac and installed it on both.
After doing all of the above, things just work! Thanks for getting back to basics. Best regards.