Maybe you should look for a copy of this book, described here, and check each of the 150 photos published there.
If there's a NASA-led conspiracy to mislead the public about Halley's comet, surely some discrepancy will turn up - and if not, then the pictures submitted by amateurs the world over will surely closely match TYCHOS predictions rather than JPL HORIZONS - and if not, then... maybe TYCHOS can't properly model comets, after all?