I just wonder why aren't you investigating existing smartphones for that. Many of them already have HDMI connection, multi core processors and can be connected with bluetooth keyboard. The software most probably will not be problem with Android (not sure about other OSes).
In my view, none of the Operating Systems available on current phones are suitable for the kind of desktop work I do. This is an actual Linux based phone, not just a Linux kernel with a VM that runs some phone apps. As a Linux hacker I feel like I could do quite a lot with this phone.
You'd need a fully fledged desktop to make it work. Is there a project like that in existence which you could just install on a random smartphone? I haven't heard of one.
