It should still be possible to simply download the free DVD, and do an "upgrade" installation. It should be able to complete the upgrade.
Otherwise, you can always do a fresh installation, but keep your separate /home filesystem, although you'll lose other customizations that are not stored below your /home folder.
Also, wanted to say that earlier: dnf uninstallation would not solve any dependency problem, it was just the cause of a totally different issue, which was mixed into the other thread, next to the "loadable library and perl binaries are mismatched" issues.
And you should probably not attempt to uninstall perl-base, you should simply rpm -Uvh all the required packages. Did you try that and could you post the output/error you got from that?
Only one other guy posted something like that, although he didn't mention all involved packages - the "had to repair perl5 update state" bullet from
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