After getting back to this tonight, I can answer my own question - it's actually easy to do in DNN because Default.aspx includes a placeholder control for style sheet linkage injection.  In the Init event handler of the server control:

Private Sub ImageEditor_Init(ByVal sender As Object, ByVal e As System.EventArgs) Handles Me.Init
     Dim CSSLinkID As String = "WESNetImageEditor"
     Dim CSSLink As String = Page.ClientScript.GetWebResourceUrl(Me.GetType(), "WESNetImageEditor.css")
     If Not String.IsNullOrEmpty(CSSLink) Then
          Dim phCSS As Control = Page.FindControl("CSS")
          If Not phCSS Is Nothing Then
               If Page.Header.FindControl(CSSLinkID) Is Nothing Then
                    Dim styleLink As New HtmlControls.HtmlLink
                    With styleLink
                      .ID = CSSLinkID
                      .Attributes("rel") = "stylesheet"
                      .Attributes("type") = "text/css"
                      .Href = CSSLink
                    End With
                    phCSS.Controls.AddAt(0, styleLink)
               End If
           End If
     End If
End Sub