Personally, I'm just calling this rig a failure at this point. It's an old pentium III unit, not a huge love loss. It was an interesting learning experience nonetheless.
Given the speed at which my Raspberry Pi boots into MAME I think you'd have a good bit of luck with Linux. I don't know enough about Linux to assist in that, or to do it from scratch myself, but if you don't reboot a lot, it can be a feasible solution. I'm sure there's a whole bunch of stuff in Raspbian that doesn't need to load for MAME to run, but that is being loaded anyway, and taking time to do so. The MAME4ALL frontend on the Raspberry Pi isn't too bad, either. It's certainly not full featured but it didn't require any configuration or set up at all.
The Raspberry Pi doesn't have a VGA out, so it can't directly run an arcade monitor, but HDMI -> VGA adapters exist, and VGA -> CGA adapters exist. If you've the spare money or parts, that could be a worthy research project.
I can say that the composite out on an RPi looks excellent on a CRT TV, with the lone exception of the interlacing.
edit: Raspberry Pi seems to support very low resolutions over HDMI, also. This would help in an effort to convert the signal to CGA.
http://elinux.org/RPi_config.txt#Video_mode_options