Hi, the only part of a cnc that I liked the linear rail support mounted the way you have done it is for the Z on a CNC router as the length is short and it is the proper way to do it given you have forces generated in all directions.
One thing that I notice on commercial lasers is that the construction of the gantry is lightweight and when you see them doing engraving at the speeds they do it becomes apparent why they need to have a small amount of mass when moving around quickly.
I would think it you continue the construction the way you are planning that you will limit your options for the machine.
For the axis that the gantry runs along I would use the linear rail that is supported, not the 20mm bar that hangs as that span is too long and it will sag.
For the axis which runs along the gantry I would use some box section and smaller rail to run the carriage on. Try to keep it lightweight as you are only supporting a light head, there are no cutting forces as there are on a router. Any additional mass here is not required and can only give you problems with accuracy when doing fast work.
I think you are right about staying with the belt and not the ballscrew.
I would seriously thing about gearing it down or at least researching if that is common. Remember a router may directly drive a ballscrew but that in itself is a gear and improves accuracy. You don't want to see the steps of the motor in your cuts but not sure if that would be a problem.
I have never built a laser so this is just based on my observations of others.