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Holocraft outputs SVG vector-image files, and then also simple mach3 compatible G-code.

Only an industrial CNC on the high-end of the cost spectrum will be able to get close to 3 microns, and only if the person running it has years of experience and background knowledge about machining works, let alone CNC machining. Some of the CNCs on the cheaper end of the spectrum  (~$50k) will easily hold a few thousandths of an inch, but if the person running it knows what they're doing I've seen parts holding about 0.001" all day. To get 10x smaller you'll need a machine that's  10x more expensive, at the very least, with cooled ballscrews and spindles to mitigate thermal distortion.

I only have experience with Haas CNC lathes and mills, and much less running a few other older machines from the 80s as a button-pusher when I was younger, and then with my own hobby tabletop build running on an Arduino that I'd like to rebuild the mechanics of someday. 

Can I ask what you're planning to do with a machine that precise? Industries that require the best possible precision, only because nothing less will do for the application at hand, tend to be the ones that buy these kinds of CNCs. For most serious industrial applications anything that can be made to hold just a thousandth of an inch is sufficient (and more affordable!)