The Ultimate Fake Book has both Gershwin and Porter - my personal favorite-, not all their songs but many of them. It may be Irving Berlin. I don't seem to recall any of his songs.
BTW There is now a "Real Fake Book" on the market; also a "Legal" and a "Legit".
WW, Leonard puts out two sizes of its' fake books, a mini and a standard. The standard is slightly larger than 8 1/2 x 11 and quite readable from a music stand. Any of the on-line bookstores can order them for you.
You are quite right about the keys; Eb, Ab, Bb, these are not your standard folkie keys.

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