Well, I think that I got my printer back up and working. As near as I can deduce from all of the research I've done, the "cups-pki-expired" error indicates that some hidden certificate ID on the printer driver is older than Cups wants. I was unable to successfully implement any solution that told Cups to ignore this date issue. Printer drivers apparently aren't monitored by the software updater and neither check for updates nor tell you when an update is available.
Epson does have Linux drivers available for my WF-7620. The Epson driver download page has several different files available, as mine is a multifunction machine. For printing, I downloaded the "ESC/P-R Driver (generic driver)" and "Epson Printer Utility" packages. Once you accept the software license agreement, you are given a choice of several files to download. There is no explicit definition of what each file is really for. Per what I found, for Zorin and other Ubuntu based linux distros, you want the "_amd64.deb" file, regardless of what type of processor your computer has (I have an Intel). I installed both of these.
Once I installed these packages, I added a new printer. I accepted the downloaded driver that it finds during the setup process. I tried going into the printer properties and explicitly pointing to the .ppd file for my printer, but this doesn't work. Every time I do this, I get an error saying "No Such File Or Directory" even though I have manually verified that the file exists on my machine.
The "print test page" function doesn't work correctly for me. I have the printer configured either to auto choose the drawer or use the main drawer, and for letter size paper. Every time I try to send the test job, it wants to pull from drawer 2, which I have configured for 11x17 paper, so I get an error at the printer. If I bypass that and let it print onto the wrong paper, the test print seems correct. Despite that mismatch, it seemed to print a PDF file correctly, pulling the right paper, so I guess this is a "successful" printer install. I'm still not sure I have full control over all printer functionality (2-drawer printer, two sided printing, etc.) but it's functional enough for now.
This process took WAY too many hours and too much of my patience. I'm writing up this detailed a description of what I did and how I solved this to hopefully save others some of the lost time and effort in trying to resolve this issue.