Any Cheap Transport from Phuket to Ko Yao Yai Island?

Hi there, my partner and I were planning to go to Phuket a few weeks later from now and we have booked a hotel in Ko Yao Yai Island, however the hotel's speed boat services are only available 4 times a day and the latest service is at 4:30PM. We'll arrive in Phuket at 6:30PM and after some research we found some private speed boat services but it'll cost 10,000 thai baht per trip which is around 380AUD! We feel like that's too much even for tourists price, so we were wondering are there any public speed boat services that are much cheaper and more convenient (doesn't stop after 4:30PM) as we would like to visit the towns in Phuket as well.

Thanks in advance!