There's actually a few good
Minnesota Beatle Project (link goes to Vol 1 at Amazon. Youtube them if you're still uncertain). Vol 1 actually has SFF and it's recommendable. I heard of them via American Public Radio (aka NPR's cool friend, and A Prairie Home Companion's host).
I found another "band" on Amazon, and there is no information about them. Anywhere. At All. Even other users are confused as to why this band, The Beatles Recovered Band is up and running. It sounds a bit more of the original Beatles recordings, but someone somewhere is trying to cash in, perhaps? There's a search engine link to last.fm, but still, no other information about The Beatles Recovered Band exists. Tell me if you find anything. So I guess I wouldn't count this as a cover / tribute band if it's a rehash of the originals?
The Nowhere Band, is based out of Florida. They performed at the Art Walk the Christmas before last, and although I didn't go, I heard that they have their act together. Unfortunately, there is quite the Liverpool foursome's songs sung, but according to the website, SFF is not one of them. Bummer.
We all know the covers done by other artists for movies and such. But with that, I say Ben Harper brought more breathy wisps into Strawberry Fields on the I Am Sam soundtrack. Jim Sturgess' version on Across The Universe, is decent, but nothing to write home about. I did see that movie solely based on I like Eddie Izzard. I am Sam is more recommended than Across The Universe, truth be told. I'm not much of a Sean Penn person, but the man does have his moments. I guess I still see him as the Vans wearing Jeff Spicoli....
At any rate, nothing beats the original Scousers. Love 'em, hate 'em, do as you must. People say I'm "too young" to know who they are and what they stood for, but The Quiet One will always have a place in my heart.