Keep "Pushing" the false report...... is there anyone else to verify what occurred that would verify his report was false ??
Personally, I would mount a few cameras that record, the guy would be served a "no trespass" warning by the kind officers, so if he stepped one foot on my property I would make sure charges got filed. It would also "record" anything in the event that was needed for "proof".
Now me, I'ld probably be setting on my front porch cleaning my shotgun every night...... and if he looked my way, I'ld just smile real big ... with a hidden camera behind me. If he says anything, just keep smiling... and wave.... saying NOTHING.