We've identified the culprit.
The server was former WG3; the migration was successful; although the WG3 registry entries were left in place and co-existed with The Major BBS v10. They were not removed and were left in place for historical (and emotional) purposes and in the event of a rollback was required.
These were ultimately causing a conflict. And since stats were working in the Stage environment (without the WG3 registry entries), once I removed them in Live, the WGSPSTAT.EXE file executed correctly, the BIN files were created, and all stats were correctly displaying on the console with the month's current data.
In summary, if you are using your existing WG3 machine to host The Major BBS v10 - whether new install or upgrade - and you want to see current/up-to-date stats in your console, and they are not displaying correctly - I recommend checking for any existing Worldgroup 3 registry entries. Use your own discretion on how to deal with them if present. Personally, I removed them and it resolved my issue.
Massive thanks to Duckula for all his patience, support and persistence whilst we dug into this.