SF really only allows you to easily edit the header, footer, logo and log-in message on Partner Portal. The rest is like a detail page. I don't believe the log-in controller for a Partner Portal will allow you to point to a custom VF page, but I suggest you check your controller to make certain. My Dev Org here doesn't have a Partner Portal for me to check; instead only a Community.
As you're already aware, you can't have Dashboards in a Partner Portal so I'm doubtful that substituting a custom VF page will provide that functionality for you. However, you can have them in a Partner Community. My suggestion would be to convert your Portal to a Community. Your current Partner Portal license will also work for a community, giving you essentially the same functionality with the added features. Before you begin building a community, I recommend you thoroughly compare the object access for read/write on the objects your current partner portal is using as there may be some slight differences between a Community and a Portal that either aren't apparent in the charts or that I've overlooked. That said, I'd generally expect your partners to get more from a community than from your existing portal.