This is a nifty tip I learned from my colleague, RCM examiner Colleen Athparia: If you keep coming to a dead halt at the barline, get rid of the barlines!
I've tried this with a few students recently with songs in triple meter, or in the above case, in 6/8 time. It works like a charm!
Of course, you want to make sure that you know your rhythms and time signature well. This is best used when you are trying to get the music flowing.