Thanks for your suggestions. It still seems as if there are some big limitations with the Drive methods (which you acknowledge in your post). Specifically, a lot of teachers utilize Forms for classroom assessments and activities. GAM won't even download Forms (it spits out a "Not Downloaded: Format not downloadable" error) and even right-clicking on the Form in Drive won't display a download option. Drive will include the Form in the ZIP file that gets downloaded if I select the Form and other Drive files to download, but it is a non-interactive HTML file, which is obviously not much use. I assume Backup and Sync will have similar issues (like you said, that's best for non-Google content). Converting Google Docs and Sheets into MS Word and Excel files during a download will sometimes produce some formatting/formula issues, but at least you get something you can work with ... not so with Forms.
I guess my post isn't much more than a gripe against Google for not having a more reliable tool to transfer files from an account in one domain to an account in another. Seems like a huge, huge oversight.
I do appreciate the recommendation of GYB ... I'll take a look at that.