Perhaps this piece taken from John King publication, quoting Bob Thomson, who has previously been mentioned in this thread may be elucidating re Peter Mulgrew experience down on the ice.
When I heard the transcript of the CVR I fell out of my chair. Most of the times Mulgrew had been there he'd gone in by sea, and all his travel from Scott Base was to the South. Hardly anybody ever went into Lewis Bay.
Had they orbited Ross Island they would have seen the cloud. If a pilot is unsure he always goes up, never down.
What Mulgrew saw or not, is no excuse for the crew to misidentify Beaufort Island, the ability to positively identify the Island was easily available, the Lat/Long readout from the AINS would have taken but a minute or two.