I’ve tried the Beverly soft drink that the OP mentioned at The World of Coca-Cola in Atlanta and it is truly as awful as everyone says. Can’t imagine anyone would drink that on purpose. A close second would be Dr. Brown’s Cel-Ray. The waiter even warned me I wouldn’t like it and it only took me one sip to realize he was right. Still, I am glad it got tried once.
As for Moxie and Big Red, those are sodas I very much enjoy!