Finally got back to this issue and wanted to report that jmcilhinney's suggested event QueryContinueDrag was the best option for my situation. I also added some code (borrowed from another site) that handled if the user moves the mouse off the form.

Code:
Private Sub UCHeadCoachSchedule_QueryContinueDrag(ByVal sender As System.Object, ByVal e As System.Windows.Forms.QueryContinueDragEventArgs) Handles MyBase.QueryContinueDrag  'Other dragdrop controls

        Dim lb As CCTrainingLabel = CType(sender, CCTrainingLabel)
        If (lb IsNot Nothing) Then

            Dim f As Form = Me.FindForm

            ' Cancel the drag if the mouse moves off the form or drops outside a eligible control
            If Control.MousePosition.X < f.DesktopBounds.Left Or Control.MousePosition.X > f.DesktopBounds.Right Or Control.MousePosition.Y < f.DesktopBounds.Top Or Control.MousePosition.Y > f.DesktopBounds.Bottom Or Control.MouseButtons = Windows.Forms.MouseButtons.None Then
                e.Action = DragAction.Cancel
                ' Other cleanup code
             End If
        End if
End Sub