Ok, in classic fashion, I managed to find the problem (this time) soon after typing out a long request for help. My system which was having the issue had (erroneous) extra arguments passed to the linter. In my case, the line in the settings file was "fortran.linter.extraArgs": ["--include-dirs ${workspaceFolder}/src/incs"]. Removing that argument causes the linter to function as normal again.
Hopefully someone else can get something useful out of this post, I guess. Otherwise, a mod can freely delete this thread if they like.