Many thanks for the beta. Unfortunately, ours was a short notice trip, and we left before your notes.
We put in at the public boat ramps at Urangan. It was the middle of the day (Saturday June 3), middle of an ebb tide, and a sunny Saturday - the boat ramp was deserted, and the parking lot near empty. At mid-tide there is a little gravel beach beside the northerly of the two quad boat ramps that we used. It was blowing 15-20 knots, so maybe that was keeping the boaties away, as it was much busier on the following Friday when we returned (light winds, high tide). Despite it being mid-tide (range ~ 2.5 m), we didn't have much current effects on the way to Big Woodie, or the next day crossing to Moon Point.
We spent the first night on the west side of Big Woodie, at the big grassy area near the north end (need highish tide to get in). The next day we sailed with a 15-20 knot SE wind to Awinya. The day after was another cruisy sailing day to Wathumba. We wanted to get away from the infernal four wheel drives so kept going north of Wathumba, but there were still 4x4s driving on the beach (which we thought was a no-drive zone) and we weren't finding good camping, so plugged back into the wind to a camp at Wathumba. Note that there is a new "no camping" sign north of the Wathumba spit; it has arrows pointing both north and south right beside a big sign saying Teebung camping pointing south. I was chatting to a yachty at Wathumba and he admitted to being the one to paint the arrow pointing south, so parks is only saying no camping north of that sign. It was blowing hard out of the south, but we found a nice sheltered site on the lagoon side of the spit just north of the no camping sign.
After a day exploring Wathumba lagoon, we faced 3 days of forecast 15-20 knot SW winds for our return trip. Oh joy. We made most of our progress when the sun was down - early morning and after dark. Paddling under a bright moon is good fun, but it was bloody cold with the SW blowing this past week!