Hey all, I think I solved it!
I formatted the external drive and changed the filesystem from exFAT to NTFS, and suddenly all of the apps that wouldn't download started working.
Not that Microsoft is very helpful about this- I had to do tonnes of research and just ended up getting a 'wrong filesystem' error somewhere else in Windows entirely. If someone from MS reads this, it would be very helpful to change the error message to 'The application you are installing requires a different filesystem' in order to make sure people find the solution right away..