Is there a way to acquire a copy of the El Capitan upgrade without downloading it first via the App Store, for example via a USB Drive? I know you can make a USB Drive after downloading El Capitan, but I am trying to skip the download itself.
Don't is my recommendation. This is how malware gets introduced into Apple software - like the Xcode ghost where developers were not downloading from Apple and not checking the validity of the software they installed.
If you call AppleCare, they might sell you physical media or even comp the shipping charge if they feel yours is a legitimate need to avoid the download. You could also find someone you trusted to have them make you an installer and ship it to you.
I have known people that went to an Apple store and asked if they could sign in to the App Store on a Mac there and download the installer to a USB drive. Since the store probably runs a caching server, even downloading 10 GB of data would proceed in a matter of minutes.
go to this site and you will get instructions on how you can download it.