A simple solution is don't let the Style dominate the performance. Changing sounds, tempo, and keys for different songs along with good vocals puts the Style more in the backround as a supporting function as I believe it was intended.
EX: One of the popular groups here ,Target, is a trio of older musicians. Guitar/Vocals, Female keyboardist/vocals and her husband on bass. They use an old Alesis SR16 drum machine and only use a handful of simple beats. No one notices because of their great vocals, dancable medelys of songs, and they SMILE while they play !!!
I listen more carefully than most and it really doesn't bother me either. They're entertaining.