Wondering if the use of "either ...nor " is correct

Would not the 'neither/nor' coupling make a double negative statement in your try?

It is not common in standard British English to the best of my knowledge (I am not a native speaker though), however used in South American English, African American Vernacular English, and most English regional dialects (taken from the Wikipedia article Double negative).

Although the following construction raises the negation count to sky-high levels, it employs usage of nor/nor (also an uncommon one), which seems relevant:

In the Harry Enfield sketch "Mr Cholmondley-Warner's Guide to the Working-Class", a stereotypical Cockney employs a septuple-negative: "Inside toilet? I ain't never not heard of one of them nor I ain't nor nothing."

With never you have to use either/or, because you can't use two negative adverbs together. In some foreign languages you can..not in English.

Mr Turchynov's version can't be criticised: "...will never be recognised either by Ukraine or by the civilised world".

The alternative form would be: "...will be recognised neither by Ukraine nor by the civilised world".

But you can't put never up against neither/nor, or the result is a cancellation of negatives, leaving the sentence meaning the opposite of what was intended.