I'm afraid that the 'port out, starboard home' explanation is nothing more than an urban legend. The very first time the word appeared in print, meaning 'grand/swell' was in 1918, having earlier appeared as 'push' - with a "u" - in a P G Wodehouse story in 1903.
As British officials and officers with wives and families had been sailing to and fro India for almost three centuries by then, it's clearly too late for the �port out' explanation to have any substance. It was also rejected in the Mariners' Mirror decades ago and presumably sailors of all people would have known.
Finally, the steamship company, P & O, themselves deny the phrase ever existed! According to The Oxford English Dictionary, it is probably no more than a corruption of Wodehouse's 'push'. It goes on to say the legend (quote) "lacks foundation".