One annoying thing about OpenSSL is its license. I hope The Better Replacement™ fixes that as well (especially if its name gets to contain the string "Libre"), and it is not going to happen by forking OpenSSL.
They are already placing completely rewritten files under ‘better’ licenses, so the license switch might happen file-by-file over a long period of time.
Is that strategy possible at all? Are there cases tested in courts (both US and EU) that assert that the file-by-file licence replacement really works?
Why wouldn't it? The author of the file will be the copyright holder by the virtue of authoring it. If she does not get rid of it, she still remains the copyright holder. Copyright does not switch owners purely by the virtue of distribution with another piece of work.
The copyright holders can later on relicense the work under something else. Licensing a work under some non-exclusive license does not restrict you from licensing it again in the future under other terms.
This is the problem with any sort of viral license in Free/Open/Libre software. Different people have different notions as to the best way of distributing it. An advertising clause is pretty minor compared to the rights you have to give away to use certain other "Libre" software.