The nature of how FPGAs work (and therefore their current limitations) mean that an original Xbox or even a Dreamcast core is out of scope unless you buy a several thousand dollar (USD) FPGA board. There is significant overhead due to the preprogrammable nature of FPGA technology and so it means that even something like Sega Saturn is a challenge on $150 hardware.
However as an avid fan of the original Xbox, I want an original Xbox core too, so when I get FPGA hardware, I am going to begin work on a rudimentary open-source concept for an original Xbox core, either on the MiSTER or Tang platform, possibly both in the future.