＞ html = Regex.Replace(html, "<script>.*</script>", "");
なんでこっちだけRegex.Replaceなんだ？

たぶん、これでいいんじゃないかな
Regex regex1 = new Regex("<script>.*?</script>", RegexOptions.Singleline);
Regex regex2 = new Regex("<noscript>.*?</script>", RegexOptions.Singleline);
Regex regex3 = new Regex("<.*?>", RegexOptions.Singleline);
html = regex1.Replace(html,"");
html = regex2.Replace(html,"");
html = regex3.Replace(html,"");