We have not been large users - 4 times?
The public ferry ran on time for us, no reservations that I know of
If you want reservations then you would need to use the private ferries that leave from across the airport - We used once - GB Express [Link is another choice]
More expensive, a little faster, the reserved times were met. I think others on this board have noted reserved times were not met for them?, but based on our 1 time trip on GB Express all went well.
Note if using a cab for a day trip on Anguilla, we checked the return boat time and took the cabs reco for when he would return to pick us up - and of course passports are needed
We liked Anguilla - different vibe
J&B