I think I’ve cracked it. I have noticed that Bali Hai does list Orgeat and Triple Sec alongside the rum and other “no juice” ingredients, so my second version without either must not be correct.
This is was based on a comment from @icecrushersd in a previous Instagram post and indeed seems to taste like the Bali Hai Mai Tai that I remember. Except that I didn’t find this too bad. Maybe I’m just so used to drinking straight rum that the tiny affordances of other ingredients is feeling like a luxury. Your actual mileage may vary.
The True Bali Hai Mai Tai
½ oz Sweet and Sour Mix – or ¼ oz Lemon Juice and ¼ oz Simple Syrup
¼ oz Orgeat
¼ oz Triple Sec
2½ oz Cruzan Light Rum
2½ oz Coruba Dark Jamaican Rum
Shake with ice
Yes, five ounces of rum.
I’m looking forward to comparing to the legendary Bali Hai original.