Just got off Majestic this morning, easy to take a taxi from the OPT: as soon as you walk out of terminal you turn back on yourself to the left, back up in lift to level 3, where there was a long line of taxis waiting. Cost to T3 was $79, which included a $10 surcharge for the port.
I'd intended to take the train from Circular Quay but wasn't sure how I'd go with changing at Central, due to maintenance, with luggage etc, so decided a taxi was the easy option! An hour after walking out of my cabin, I was through security at the airport, let's hope rest of the day goes as smoothly 🤞