So I eventually found a work-around for this which I’ll pass on in case its useful to anyone else in the future.

Support for EXFAT on mac seems a little sketchy (its easy to set up read support, but seems to need a lot more fiddling in order to be able to write). EXT4 and NTFS do work but they’re not formats OSX can read by default. However it doesn’t matter because it’ll be the router reading the drive, not your mac.

You just need to format the drive in one of these formats. There are a few methods for doing this but ext-fs offers a free trial mode (hopefully you’ll only need to do this once). Attacht he drive directly to your mac and install the software. Then format the disk in EXT4 format either from disk utility or from the ext-fs pane in your system preferences.

Reattach it to the router and you should now have read and write support.