I think I have come up with a fairly likely reconstruction. One thing to keep in mind is that there is a serious discrepancy in what the Kennedy crew claims about when Kennedy came back to the cottage to ask for help and what the time would have had to be according to the well-based estimate of the deputy who reported seeing the two in the car at 12:40 am.
They see the uniformed deputy approach them and Kennedy takes off, not wanting to be caught in her company under these circumstances. He says as soon as he is out of the deputy's immediate sight: "Take the car and I'll walk back to the cottage and get a ride to the ferry." (I don't know what the distance was but it was not far, the deputy saw three people from the cottage strolling along the highway in the immediate area and that was a ten minute walk from the cottage, according to this link. Kennedy may have known the ferry was running longer than usual that night, or may have known he could have hitched a ride on someone's boat.)
He walks back to the cottage and has LaRosa wake up the other two to carry him to the channel where they can row him across, explaining why he separated from Kopechne. If she had returned by this time in his car they could have taken him in it, but it would arouse no suspicion if she did not make it back immediately. They remember the time as about 12:20 when according to their story Kennedy got them up and they went to the sunken vehicle.
According to the link below two policemen walked from the bridge to the cottage and it took them 23 minutes. Despite Kennedy's claim the time of the accident was at about 12:45 am according to the testimony of the deputy, whose presence was attested to by the three walkers from the cottage. If Kennedy had been involved in the accident at 12:45, made repeated attempts at rescue til he was so tired he had to rest for 15 or 20 minutes, and then walked at least 23 minutes back to the cottage there is no way he would have erred so greatly on the time. As it was, he had no particular reason to remember the time and when pressed gave what he thought was a rough estimate without thinking of the consequences.
For some reason it is important to Kennedy to be on the mainland bright and early, a meeting or something, so the two friends carry him to the crossing and, the ferry now having stopped running, they carry him across on one of the many boats lying about and return to the cottage, none of the three having any idea of any accident. Kennedy enters the hotel and, since he is tired and must be up early, he complains to the night clerk about the noise and goes to bed. He is seen conversing normally the next day until he gets word from the island after which he seems thunderstruck, perfectly natural and unfeigned conduct.
The two friends return to the cottage and go back to sleep, having no reason to give a thought as to whether Kopechne had come back or not. When they get the news and go to the mainland to get Kennedy and say on the ferry, "We just heard about the accident ourselves," they are telling the truth, nobody has started to lie yet.
When he gets the news Kennedy remembers that a uniformed policeman had observed his vehicle and would remember it and for all he knows recognized Kennedy himself, moments before the accident. Panicking, he thinks it would sound better to admit having been in the vehicle at the time it went off the bridge than to explain why he got out but they do not have time to work out details of the story before they are surrounded by police and news people, and the tangled web has begun and can't be undone.
This basically is the same hypothesis as in my first post (one that has been out there for a long time), other than the idea that the reason Kennedy returned to the cottage was to get a ride to the crossing, completely unaware of the accident.
http://www.cwporter.com/ytedk3.htm
