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Actually neither Yahweh or Jehovah is “impossible” as you put it. We know none of the proper names in the Bible are correctly pronounced by us today particularly since we use “J” as Hebrew used “Y” and “I”. No one two thousand years ago would recognize “Jesus” as a name and even today proper names are pronounced differently in every language.

Some further information on the subject:

“Handling the Tetragrammaton in English Translations
By Alan Whitby
(Bible Collectors’ World – Jan/Mar 1988)

However, Rotherham was not the first in print with Yahweh. Just one year earlier in 1901* James McSwiney’s translation of the Psalms and Canticles used the form YaHWeh on occasion. If McSwiney should prove to be first this is perhaps a little unfair on Rotherham. His OT translation was already completed by 1894, when the publication of Ginsburg’s Critico-Massoretic Hebrew Text caused him to delay publication to revise the whole work. 11
Since the turn of the century many others have followed these examples. The Colloquial Speech Version (from 1920*) published by the National Adult School Union used Yahweh. So did many translations of portions, such as S. R. Driver’s Jeremiah (1906), Gowen’s Psalms (1930), Oesterley’s Psalms (1939) and Watt’s Genesis (1963). The 1960s saw a number consistently use this form including the Anchor Bible (from 1964) and the popular Jerusalem Bible (1966).
A. B. Traina’s Holy Name Bible (1963) uses Yahweh, and is also consistent in Hebrewizing other names as well. In Traina’s NT (1950*) Jesus is Yahshua. 1979 saw the commencement of Kohlenberger’s NIV Hebrew Interlinear using Yahweh. Additionally, many popular versions that use LORD have chosen Yahweh for Exodus 6 v. 3, including An American Translation (1927*) and the Basic English Bible (1949*).
www.biblecollectors.org/articles/tetragrammaton.htm”