How do I create securely password protected .xls files in Excel 2010 from VBA

I found that in Excel 2010 (and 2007), when you try and choose one of the more secure types of encryption, it seems to silently ignore your settings, leaving you with a file that can be cracked in seconds at decryptum for example.

This does not apply to the new file formats that are AES encrypted by default, only when you are saving down to the 97-2003 format.

This is the macro I create in the workbook:

Sub enc()
  Me.SetPasswordEncryptionOptions _
    PasswordEncryptionProvider:= "Microsoft Strong Cryptographic Provider", _
    PasswordEncryptionAlgorithm:= "RC4", _
    PasswordEncryptionKeyLength:=128, _
    PasswordEncryptionFileProperties:=True
  Me.SaveAs _
    Filename:="encryption_test.xls", _
    FileFormat:=xlExcel8, _
    Password:="password"
End Sub

It is quite easy to get Excel 2003 to (correctly) output with these encryption settings by omitting the FileFormat parameter:

Sub enc()
  Me.SetPasswordEncryptionOptions _
    PasswordEncryptionProvider:= "Microsoft Strong Cryptographic Provider", _
    PasswordEncryptionAlgorithm:= "RC4", _
    PasswordEncryptionKeyLength:=128, _
    PasswordEncryptionFileProperties:=True
  Me.SaveAs _
    Filename:="encryption_test.xls", _
    Password:="password"
End Sub

decryptum then fails to decrypt as I would expect.

Am I doing something wrong or is this a bug? If it is a bug, how do I work around it?

I've added a solution of sorts for Excel 2010 below, but I'm hoping for something simpler, and preferably something that works for 2007 as well.