There is an alternative.
If you had an AIO- All In One (built into the screen, so no more space required) computer running windows, and connected via network (wireless if desired) to the Linux computer to run ssh in a window from the windows box. This way, you would have your Linux stack running natively and your windows machine running natively. If required, you can connect the Linux video via HDMI to your AIO monitor and use ur wiress keyboard and mouse. However, it does still seem the long way home (more expensive).
Again, the specifications seem arbitrary. If you could state specific objectives (compile whole linux distro and build into package over night or in 4 hours.
The more I read this thread the OP is hell bent on having linux run as close to bare metal as possible. This solution achieves that desire. What I would do and I agree with most posts saying run Windows (2000 - 8.1-depending on task) and then Linux in a VM such as Virtual Box. That is the easiest and most usable route. I like having an XP VM just in case. Since it doesn't get any more updates, it is very stable for private a network.
The reason so many advocate this solution is that windows graphics run best on a windows machine. The VM video interface just works better for that combination with windows as the host. Most video cards/ devices are designed to run DX* (windows API). Using DX* to emulate OpenGL is easier as more info is available. Since the GPL conflicts with IP ownership to most graphics companies, they are not real keen on supplying chip level commands/access/ documentation. Without access to the hardware documentation, Linux drivers have trouble supporting the windows DX* graphic API. Yes I heard Nvidia say they are going to play nicer. Wake me up when you see a finished combination. Yes they support Open GL, which is great.