This thread got me halfway to configuring Julia to update packages through my work network. The missing piece was adding my workplace's security certificate to the list of certificates used by my git installation, which is very well explained in
this post.
After doing the above, I got an error saying "SSL certificate problem: unable to get local issuer certificate". I then made a copy of the ca-bundle.crt file in my git folder, copied the plain text from my company's cer files into this copy and ran
run(`git config --global http.sslCAInfo C:/Users/ngudat/ca-bundle.crt`)
The whole thing is running rather slowly now and my CPU is running at max during Pkg.update() because of a host of on-access scanners and "privilege guards" scanning the traffic, but at least it's working!