Create a shortcut/widget to an Accessibility feature
If you go into General -> Accessibility -> Accessibility Shortcut, is there an option to add 'Stream to left hearing device'?

If so, you can then triple click on the home button and that should (providing you haven't enabled any other accessibility features) toggle the stream. 

Unfortunately I do not have a MFI device to test this with, however I do use the accessibility shortcuts frequently.