Look up BST motion -
https://bstmotion.aliexpress.com/store/314742 they have a house brand and Hiwin. I like the way you have built the machine in a box very stiff. You do need to specify "high preload" for the cars. Normally they are supplied in "zero preload" which will get small wobbles as they wear over time especially on a mill.
The rail stiffness is a function of its foundation more then the rail itself. So you will only be as stiff as the extrusion. You have taken advantage of the supported rail in your design, with square rail you will need something under it. If you keep to your first concept then round is the go... at least on the table rails...
You also have long bearings on the bottom of the Z axis rails. That was a very good move as these are the highest loaded bearings in that type of machine as they take the impact loads from the tool. In square rail you can get long bearings but using high preload is the go to resist the tool loads better. Peter