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