I lived in Palau for two years and visited again last summer. There are GTs there, but you've got to get away from Koror. Most of the big ones are caught up north. Also, you'll have A LOT of shark bycatch.
There are captains who cater to GTs, but I think they are mostly Japanese and I struggled to find any information on them last year. You could check with NECO Marine, if for no other reason than to get a guide suggestion. The owner of NECO is hardcore fisherman, but I'm not sure how much GT fishing he does. Stay away from Sam's Tours.
There is a guy on here who currently lives in Palau. I remember he made a post in the "Show us your boat" section.