As detailed above, the plan will vary depending on when we reach House Lothston's docks. If it's night before we get there, Timon won't be going ashore to talk to the harbor master. In either scenario, by a "short rest" I mean just enough so that the men's performance won't be impacted too heavily. I've assumed that's about four hours, but I leave that in your hands to decide.
As for detecting anchored ships in the night, wouldn't it be reasonable to expect anchored vessels to have a lantern lit for crewmen on watch? Of course, Longpalm may elect not to do so if he's being paranoid, but at least we would have good odds of finding (and avoiding!) boats that aren't
engaged in criminal endeavours.