Well, it turns out the problem was caused by a change our network technician made on our network. Whatever he did has been corrected, and so the issue is now resolved.
*EDIT*
Recently did a fresh install of Windows 10 b1709 on a laptop, then installed the latest Firefox (57.0.2) and Chrome (63) per normal. Was able to install Adblock Plus in Chrome without any issues, but when attempting to do so with Firefox I get "Insecure connection". Specifically:
Clicking 'advanced' gives me the following:The owner of addons.cdn.mozilla.net has configured their website improperly. To protect your information from being stolen, Firefox has not connected to this website.
I've tried through Adblockplus.org and through the Add-ons screen in Firefox itself. I even tried selecting uBlock Origin from the main Add-ons screen, to no avail (the latter says 'Download failed. Please check your connection.'). I've tried uninstalling and reinstalling Firefox, I've tried deleting the cert8.db file from Appdata as well as verifying the time/date is set correctly (it is), all to no avail.addons.cdn.mozilla.net uses an invalid security certificate.
The certificate is not trusted because the issuer certificate is unknown.
The server might not be sending the appropriate intermediate certificates.
An additional root certificate may need to be imported.
The certificate is only valid for search.dnsadvantage.com
The certificate expired on Sunday, September 17, 2017, 11:03 PM. The current time is Wednesday, December 20, 2017, 11:53 AM.
Error code: SEC_ERROR_UNKNOWN_ISSUER
To me, this appears to be an issue on Mozilla's side, but since I saw no one else mention it on the forum (through a limited search), I thought I'd post in case someone had a suggestion I hadn't considered. Thanks in advance.
In the meantime, I'm going to attempt to install version 56 and see if that resolves my issue. I'll post back if it does.