... An Umlaut replaces an "e" after the vowel, as in Lueders. ...

You remind me of the common way of substituting for an umlaut

"Boehler" rather that (phonetic representation of the common
pronounciation) "bowler".

The "umlaut'ed" vowel sound is unique, isn't it? Not literally
represented by removing the umlaut and suffixing with an "e"?

That was alright. Turkish was "the greatest fun". Full respect for
the language. I could never do more than catch buses, shop, order
meals, etc., extend greetings and simple invitations - but actually
rendering those in a conversational way which blended into the flow of
everytday events... Lots of sounds in this Middle Eastern language
which we don't have. Then their best - they have all these grammatic
rules so that say two words convey what we need seven to do - and the
vowel sounds harmonise through those words. The mind was on a really
thrilling twisting multi-dimensional ride flying all that while you
responded to someone who asked if the chair here was free (would they
be invited to share this table in a cafe full of people having
breakfast on their way to work), etc.

Regards,
Rich S

PS - I will try to understand your technical challenge / question.
Tired after a working week.
Bit later...