I'd like to know if there's a Japanese equivalent to the Jerry Springer show
I don't know of an equivalent to Jerry Springer but Eigo de Shabera Night is a Japanese Talk show. Personally I don't watch talk shows like Jerry Springer, Oprah, etc... so I don't really know much about them. Though this show is more so a late night talk show than tabloid talk show. Summary:
http://www.nationmaster.com/encyclopedi ... bera-Night
Of course for your fic you could just use the Jerry Springer show. It was on Japanese television after all (also shown in England, Australia, Italy, the Netherlands, Ireland, New Zealand, Poland, Hungary, Hong Kong, Portugal, Serbia and South Africa - according to local Fox channel program guide).