Maybe not un-readied but timer reset would be good, especially useful to those who change ship late just because they're short on time and still learning the ropes, all too often does it pose a problem learner pilots changing last second due to a basic lack of time thanks to the pub "ready up scrub" attitude...
Reason for unready is because otherwise the lobby will start in .. is it 5? secs cause everyone is already readied up.. If half are then 30sec lobby start.. You can't easily reset-the timer and avoid this without unreadying people..
As for player changed due to needing time.. This would only benefit them, as now they have a min more.
Granted it does cause the issue of people trolling with it by constantly changing ships creating an endless lobby... which wouldn't be easily addressed..
Maybe not a default 60 second addition. If there was a change, the Add Time button could become active with an indication that a ship changed. Then it is your choice on whether you need to add time or not. Otherwise, this could be abused quite a bit.
Issue would then be, if its very last sec, do you have enough time left to see the change and click the add time button? Is it worth the effort to put it in, if it can be easily bypassed? Adding any amount of time will cause the same issue of troll guy switching his ship often enough to create an endless lobby..
Maybe a better thought is, you can't switch ships if you ready up.. This way you can easily tell if a ship is able to try to last sec switch. Coupled with the topic idea(which is useful for more then last second switches in general) might be sufficient to spot and deal with last second switches with out more complicated systems..
Another idea is if you last second switch, your ship becomes locked and unreadied and time is reset to 30secs?.. This way you stop the lobby from starting quickly (30 secs is given) only once per ship per lobby and you can no longer switch your ship so you can't try to do it twice in the same lobby..