Thanks Shona, and like annD, something for my 'later' list.

Sorry Shona. It certainly wasn't my intention of "steal your thunder".
I knew about 'Trinity Bay' because I tried to book a trip on it myself a few years ago but they were booked out for the period I wanted to travel.
Instead, we did a 2 day light plane trip from Cooktown, staying overnight at Horn Island at the Gateway Resort (the place with the museum). Like you, we took the little ferry to TI for a look (we were there on a Sunday too) then next morning we landed on the beach just a few hundred metres from the cape and walked to the tip. We then returned to Cooktown, stopping at Musgrave for lunch. Whilst at Musgrave I talked to a few people who were returning from Cape York in their 4wds and I reckon going by boat or plane is certainly preferable to enduring days and days of corrugated road.