Edit: pro tip: make sure you get the IP addresses right so you won't spend days chasing after a trivial error like some idiot. Don't ask me how I know. Thanks to @Arlos for pointing that out.
I ended up ripping the HDDs and putting them on my server, then proceeded to share the drives as normal. My docker containers now use them perfectly fine. IDK wtf Synology is doing but it's cumbersome AF.
As a wild guess, try completely specifying the IP address in your fstab instead of relying on a wildcard. Wouldn't be the first time there was a slight difference in how a marginal feature like that worked in different contexts.