It looks like I may be getting somewhere with customer support. Sometimes support eMail addresses don't accept replies, so I wasn't sure if I would be able to update my ticket that way, but it looks like PW does get them. The response indicated that my issue has been "escalated it to the next tier of support for further review." It also stated that they are aware of the website's redirect loop and are working to fix it.
I am cautiously optimistic at this point.
I have the same problem as you, only with one stuck ship, there is a work around, it's not perfect, but it may help
1. Change the name of the stuck ships to ZZZZ, or whatever makes them alphabetically last in your ship list, this will prevent their bridge slots from overriding ships you can use.
2. If you can discharge your shuttle, (Hopefully it's one you can reclaim later) you'll find that switching to small craft will give you access to one of your stuck ships, and also allow you to use its bridge slots as well.
I hope you can get it fixed. I made a ticket a while ago, nothing ever came of it, and so if your problem gets fixed there may be hope for me and others with this problem
Thanks for the workaround. It's a dirty, dirty hack, but it works in the meantime. I don't think I'll be able to use the two frozen ships until a real fix gets made, but at least now I can use one of my ships.