Can we list the potential ways of transliterating Polish Ashkenazi בֵּית, בֵֿית, פֵֿא

[Channalee]

In the book I cited, "ey" makes the same sound as in the English words "grey" and "prey."

So that's [ej], then. can we get some transliterations for those letter names with [aj] (English long-i sound)?

In that same book that I cited, they transliterate Yiddish words with the "English long-i sound" using the letters "ay."
 
There's also an old (and much-beloved by Americans) book by the late Leo Rosten titled The Joys of Yiddish and, in it, Rosten generally transliterates the "English long-i sound" with the letters "ei"  (as in gesundheit).  Rosten generally transliterates the "English long-a sound" with the letters "ey" or "ay" (as in treyf or trayf).

Newer editions of Rosten's book provide both Rosten's original transliterations as well as the YIVO standardized transliterations.
 
The original Yiddish transliterations in Rosten's book are supposed to favor the southern dialect ("Poylish") pronunciation of Yiddish – which is representative of Jews from Poland to Romania and the Ukraine.  This is also the dialect that was preferred for the Yiddish theater in America.