You are interesting to read.
1 This sentence is false.
2 This sentence = "This sentence is false"
Since sentence 2 contradicts the law of identity sentence 2 is false.
Therefore sentence 1 either has no defined subject, or breaks the law of identity.
SO: The paradox cant be derived.
Note. A computer should use the test to exclude the predicate "false" from self referencential use.
Its probably too tecnical for me to really understand... But I suspect my results (if correct) will affect this class of problem.
PS This insight of yours is unusual:
"Having the solution for formal logic already, it's easy to forget the more general issue."
One cant study the anatomy of paradoxes in a system that doesnt allow self referemce