Exchange 2013, multiple IIS OWA sites with different authentication

Question

Hi
I have an exchange 2013 server with Client Access and Mailbox server installed. The server has an second ip address which I have bound an additional IIS site to. The additional IIS site is named ExchangeExternalFBA.
The default web site is configured for basic and windows authentication with:
Set-EcpVirtualDirectory -identity "ecp (default web site)" -FormsAuthentication:$false
Set-owavirtualdirectory -identity "owa (Default Web Site)" -FormsAuthentication:$false -WindowsAuthentication:$true -BasicAuthentication:$true
Then a new ECP and OWA are configured with:
New-ecpVirtualDirectory -WebSiteName "ExchangeExternalFBA"
New-OwaVirtualDirectory -WebSiteName "ExchangeExternalFBA"
Set-owavirtualdirectory -identity "owa (ExchangeExternalFBA)" -LogonFormat FullDomain -FormsAuthentication:$true -WindowsAuthentication:$false -BasicAuthentication:$true
Set-EcpVirtualDirectory -identity "ecp (ExchangeExternalFBA)" -FormsAuthentication:$true
Then I perform an iisreset.
My problem is that then when I try to access the ECP or OWA on the default website, it loads forms authentication! The ECP or OWA on the ExchangeExternalFBA web site works correctly and also loads forms authentication.
If I run...
get-owavirtualdirectory "owa (ExchangeExternalFBA)"
then it returns:
InternalAuthenticationMethods                       : {Basic, Ntlm,
                                                      WindowsIntegrated}
BasicAuthentication                                 : True
WindowsAuthentication                               : True
DigestAuthentication                                : False
FormsAuthentication                                 : False
LiveIdAuthentication                                : False
AdfsAuthentication                                  : False
OAuthAuthentication                                 : False
If I then run
Set-EcpVirtualDirectory -identity "ecp (default web site)" -FormsAuthentication:$false
Set-owavirtualdirectory -identity "owa (Default Web Site)" -FormsAuthentication:$false -WindowsAuthentication:$true -BasicAuthentication:$true
and perform another iisreset then when I try to access the ECP or OWA on the default website it loads correctly. But then the forms based authentication on the ExchangeExternalFBA website can no longer log in, it does not accept the user name and password.
If I then disable and enable FBA on the ExchangeExternalFBA website then it works but forms based authentication takes over the default web site again!
Whether I perform the above from the gui or from powershell it does not make a difference, the same behaviour is observed. Changing the logontype on the FBA does not make a difference.
This has been tested on exchange 2013 cu1 and cu2.
Similar(if not identical until they get sidetracked) issue reported in http://social.technet.microsoft.com/Forums/exchange/en-US/9fcd360f-6658-4940-add7-2f13265cf86b/multiple-owa-sites-on-a-single-server-2012-with-exchange-2013-mailbox-cas.
This worked fine in outlook 2007 and 2010, why now do my virtual directories break each other?
I can reproduce the issue on a test exchange 2013 I built in dev.
Is this a bug or are you no longer meant to host different forms of authentication on a single cas?
I'm mostly interested to see if this works for other people and why it no longer seems to work in 2013, so please no questions; 'why do you want 2 different forms of authentication'. 
Much appreciated, Thanks!

Answer 1

Based off of your feedback I have run the following:
Remove-OwaVirtualDirectory "owa (ExchangeExternalFBA)"
Remove-EcpVirtualDirectory "ecp (ExchangeExternalFBA)"
iisreset
Set-EcpVirtualDirectory -identity "ecp (default web site)" -FormsAuthentication:$false
Set-owavirtualdirectory -identity "owa (Default Web Site)" -FormsAuthentication:$false -WindowsAuthentication:$true -BasicAuthentication:$true
New-ecpVirtualDirectory -WebSiteName "ExchangeExternalFBA" -Role ClientAccess
New-OwaVirtualDirectory -WebSiteName "ExchangeExternalFBA" -Role ClientAccess
Set-owavirtualdirectory -identity "owa (ExchangeExternalFBA)" -LogonFormat FullDomain -FormsAuthentication:$true -WindowsAuthentication:$false -BasicAuthentication:$true
Set-EcpVirtualDirectory -identity "ecp (ExchangeExternalFBA)" -FormsAuthentication:$true
iisreset
After this there has been no change in behaviour. After the iisreset, forms have again hijacked the default web site and re-setting the authentication on the default web site removes the forms but breaks the ability to sign in to the forms based page on the
ExchangeExternalFBA web site again.
Note. '-Role Frontend' did not work. It showed the error:
Cannot process argument transformation on parameter 'Role'. Cannot convertvalue "frontend" to type
"Microsoft.Exchange.Management.SystemConfigurationTasks.VirtualDirectoryRole".
Error: "Unable to match the identifier name frontend to a valid enumerator name.  Specify one of the following enumerator names and try again:
ClientAccess, Mailbox"
    + CategoryInfo          : InvalidData: (:) [New-OwaVirtualDirectory], ParameterBindin...mationException
    + FullyQualifiedErrorId : ParameterArgumentTransformationError,New-OwaVirtualDirectory
Running get-help New-OwaVirtualDirectory -detailed shows the correct usage would be '-Role ClientAccess'?
    -Role <ClientAccess | Mailbox>
        The Role parameter specifies the configuration that should be used
        when the virtual directory is created. The following are the values
        that can be used with this parameter:
        * FrontEnd Configures the virtual directory for use on a Client Access
          server.
        * BackEnd Configures the virtual directory for use on a Mailbox server.