Well, I uninstalled Tacview, deleted the files that I used to manually install the exporter, and reinstalled Tacview on to the same HDD. This time the exporter installed automatically, but I'm still not getting any ACMI files recorded...
Checking the logs I see this:
00154.336 INFO TACVIEW.DLL: Tacview Flight Data Recorder 1.6.0 Loaded
00154.336 INFO TACVIEW.DLL: Config={dataRecordingEnabled=1,recordClientsSessionsEnabled=0,bookmarkShortcut=0,playbackDelay=600,profilingPeriod=600,debugModeEnabled=0}
00159.198 ERROR TACVIEW.DLL: Failed to create flight data recording [C:\Program Files (x86)\Tacview\ACMIs\Tacview-20170516-001344-DCS-F-5E QuickStart - Takeoff.zip.acmi]