[Avodah] ROSH HASHANA and YK: Hee-ne-ni--"Tefilla Acheret Lechazanim" query (2nd attempt)

[Noah Witty]

With minor changes for transliteration and typos, I received the 
following inquiry:

"A matter of curiosity regarding the 'tefilla shel shaliach tzibur' 
before Musaf on Rosh Hashana and Yom Kippur:

"In the older machzorim printed in Europe and the US, there is an 
additional tefilla after 'Hee-nneni he'ani me-ma'as.'  In the Machzor 
Rabba that I have, it is titled: 'Tefilla acheret lechazan' and is in 
small letters. This 'tefilla acheret' does not appear in the Rinat 
Yisrael Machzor at all. Perhaps you can find out something about the 
tefilla. When was it written?  By whom? And when?  And why was it 
included/excluded from the machzorim??"

Thanks in advance.
Noach Witty