Carbon fiber instead of smooth steel rods?
Steel is the best material for a linear rod when you have a fixed cross-section. It will have the least flex of any rod (aside from some exotic metals) of the same size.
Carbon fiber's material properties might seem superior at first sight, but the stiffness is very anisotropic -- it's very stiff along the grain and not very stiff across the grain. So multi-axis stresses like bending aren't necessarily going to perform up to the theoretical specs. Carbon fiber has exceptional stiffness-to-weight ratio, but the stiffness-per-area isn't necessarily superior in this application.
People do occasionally use carbon fiber for linear rods/rails, but only in much larger sizes than 8 mm. Think >25 mm.
And that's really the problem here. 8 mm diameter at 550 mm long is well outside what's reasonable for bending stiffness. Bending deflection increases with the CUBE of length, and this is simply far too long for the size of rod. The general rule of thumb for precision motion applications is length < 25*diameter. That's a conservative rule, but it's the right ballpark. You really shouldn't be going over 200-250 mm or so with an 8 mm rod.
Thank you very much for the info! 2020 V-Slot extrusion should behave way better (that is, the bending should be almost negligible) right?
I could only add that you can try to use kinda print leveling feature. That's not the solution for bending rods of course but you can decrease the influence of it.