Hello Anders,
Regarding the second option - I'm just trying to create the same setup on my side. When done I will be able to directly provide you screenshots or we can have also an online SAPConnect meeting.
Regarding the first option - the users from the thin client can access the same redirect application but with parameter "spnego=disabled" (https://sapasjava.company.com/redirectapp/index.jsp?spnego=disabled&...) and in this case they won't be logged in as PC123 user but will see a logon form. Perhaps it is still worth considering also this option.
Regards,
Dimitar