How to backup one external drive to another, using a Windows PC with limited permissions?

I have an external drive most of my work is on, and I use it at a work PC running Windows 7 Enterprise with limited permissions (small research team in a big organization).

I want to make sure that the 1-2TB data on my main external drive (my 'expansion' drive) is backed up, at least once a month. It is essentially my local filesystem that I work on. Aside from program files I keep very little on the PC's built-in drive. This is because I need way more storage than available on the built-in drive, and this enabling me to move and work on different machines as occasionally needed.

I was doing backups using Windows Backup & Restore, which enabled me backup files from the expansion drive to a backup drive when both are plugged in. This appears to work, but I'm finding I can't restore files: on my usual work PC I think because I lack administrator permissions (I get an error "either a required impersonation level was not provided or the provided impersonation level is invalid (0x80070542)") and on another PC without strict permissions I run into a different issue, maybe due to what I explain in the next paragraph (the error is "The system cannot find the path specified (0x80070003)").

The drive occasionally changes its ID (eg. one week it is G:\ the next it is H:\ ) because I am moving drives around. Automatic or incremental backup needs to account for that.

I am thinking to just drag-and-drop data from my expansion drive to my backup drive in Windows Explorer once a week or once a month to get a low-frequency incremental backup going. That seems like a clunky solution however since it a) relies on me remembering to manually kick that process off, and b) it is a lot of data to drag-and-drop.

How can I backup one external drive to another, using a Windows PC with limited permissions? Is my drag-and-drop solutions feasible, and are there any better (faster, more reliable, more automated) methods? Backup frequency should be at least once a month - the more the better but if it slows work down, that isn't better. Most work in the process month to month is restorable from emails, thumbdrives, and/or cloud storage that we move files around on when actively working with them.

Asking how others in my office deal with it, their responses are hopeful but not substantial.