If you're on a liveaboard,you may already get some land time on Pelilieu. We didn't get there when we did the Aggressor years ago, but we did on our recent trip on Ocean Hunter 3. About half the group did an island tour while the rest of us just hung out and explored on our own.
For a kayak trip you're probably looking at an all day excursion with lunch. (Longer is better there's lots to see.) So I don't know that you would do that and also rent a car to tour around. Getting picked up or dropped off by whatever operators you're working with between the liveaboard and any tour shouldn't be a problem. And you'd want to verify with the ops but I think at least Sam's or Fish & Fins would allow you to leave luggage if you're out with them. (Safe is another matter - I don't recall if they really have a secure place it might be more of a pile it up in a corner thing.) Or if you book a room for the day someplace they might transport your luggage there for you, and the hotel could put it in your room when available. Thing is, you'll still have a fair amount of time after the tour, assuming you're on the 0'dark hundred United flight. It's a drag to pay for a hotel for the few hours you would be using it. But the ops will close at some point, and hanging out at the airport all evening for a 1am flight isn't any fun (assuming you even can.) A hotel gives you a place for your luggage, and a base to clean up, change, go eat, repack anything etc. before heading to the airport.
Alternatively, you might be able to get taken to the airport, rent a car, keep your stuff in it while kayaking, clean up at the op, explore a little, then kill time with a very long dinner & drinks someplace. We haven't actually tried that but it might work ok. I assume any car rental place there has a way of dealing with odd hours stuff, since it's all odd hours.
