Hi Barney,
I understand that you want a custom login page, but want to use the windows credentials for authentication.
This can be done easliy using the LDAP Membership provider. You can extend the web app to a different zone and configure FBA authentication.
Follow this MSDN article which gives detailed steps to configure LDAP Membership provider.
https://technet.microsoft.com/en-us/library/ee806890.aspx?f=255&MSPPError=-2147217396
Hope this helps.
Ram Prasad Meenavalli | MCITP | MCTS SharePoint | MCPD SharePoint | http://www.spdeveloper.co.in