In this approach, I've added the phrase Please specify. This actually may be a bit confusing to the user because there's a disconnect between the "Other" field and the phrase "Please specify". The word "Other" should ideally be part of the label.
In this approach, I've marked up the word Other with two nested LABEL elements. I've also added a debug phrase (Ignore this text) to test whether JAWS is getting its label from the markup or by intuiting that the field's label must be the text that immediately precedes it. As it turns out, this solution works for JAWS 6. JAWS reads "Other" both for the radio button, and for the text field.