Thank you everyone for your help! I imported my ADE authorisation from WINE into the DeACSM plugin, and now I'm able to download my book.

The only "downside" of this method is that since I have DeDRM configured already, Calibre seems to automatically discard the original encrypted e-book and only add the decrypted one to the library. Since the encrypted book can only be opened in Calibre and ADE, I don't think it really matters, though.
The only other possible solution I could find was in this GitHub gist, which indicates that ADE 2.0 lacks TLS 1.2 support by default:
https://gist.github.com/bmaupin/65ef...b897f2224dfa38
I'm not going to bother making a Windows 7 VM just for ADE though, since DeACSM already works. Hopefully if anyone else has this problem, this thread might be a helpful resource on how to address it.