Cnc is fundamentally different from 3d printing in that the tool head and workpiece apply significant forces to each other. You need rigidity to deal with that and belts don't provide it.

A CNC for what, milling? If so, I agree with the others here. Using belts to drive a milling machine is likely to result in too much backlash to be viable. The entire point of ballscrews is that they're (reasonably) proof against backlash, even moreso than regular lead screws. We can get away with it on our printers because in normal operation the print head and nozzle are never supposed to touch anything so it doesn't matter. For milling, backlash in your movement system will cause your tool to kick itself off of the workpiece when its edges touch it (i.e. hundreds/thousands of times per minute) which will make it chatter, result in lousy finishes and accuracy on your parts at best, and most likely wind up with you breaking a lot of bits.

Maybe you could get away with it if all you're doing it routering wood, or something. The moment metal enters the equation, forget it.

The key to milling is rigidity, rigidity, rigidity. If you are having chatter problems, accuracy problems, tool breakage problems, basically any kind of problem, nine times out of ten you'll wind up tracing it back to backlash and/or your machine or clamping arrangement not being rigid enough in some capacity.

Steal inspiration from the RIGCNC project. A number of people have built them (myself included) and if you go digging through the internet archives for the site, there is a pretty good writeup about why it was designed the way that it was. It could be a useful launching point for your own design.

I dug up the writeup here: https://web.archive.org/web/20230421201903/https://www.rigcnc.com/

i can't really be of much help, but if was thinking out loud:

• I don't think belts can handle the cutting forces, they will also stretch which will (maybe) ruin the part, create chatter, snap bits etc.
• the old standard for small milling machines is that you move the work, so you use an XY table, like you find on the taig and sherline. if you went this route, know that they make ready made xy tables, you might find them in machinery shops. that might make things cheaper.
• why not make a voron cascade? at least you know it has been thoroughly tested. you only need one ballscrew for each axis.

Yes, "bedslinging" is the proper way to build a milling machine for metals. Gantry designs exist for CNC woodworking, but are uncommon for metal.

Do not use 2 leadscrews per axis. You cannot time them well enough to prevent binding over long moves. If you are worried about moving the mass with the motors and leadscrews, buy bigger ones. The best way to drive the Y axis is with another stepper and leadscrew.

You can drive ballscrews with belts if you need to offset the motors. But your belts need to be as short as possible and as stiff as possible. Otherwise you will lose steps and make junk rather than functional parts. So no long light duty toothed belts like 3D printers use.

And when thinking about motion despite what your eyes tell you, it's always the tool that moves and not the part.