Is it okay to have a PCI-e back panel missing from the case?

Solution 1:

Yes, it ought to be safe. Those plates are sometimes referred to as "dust covers" (or "slot covers"). If you don't have the plate covered, there is a larger opening that dust can enter the system. (Fans usually aren't pointed at the slots to blow dust out in that direction.) It's also big enough that some bugs might be able to crawl in. Admittedly, that seems rather unlikely. However, it is more likely than if the dust cover was still blocking access.

Another option is to just buy any expansion card... maybe more USB ports, or a network card, and simply cover the hole that you made. However, if you don't wish to do that, I wouldn't worry a whole lot about it. Many systems have a slot cover missing.