Center support for vertical blinds

I am replacing the broken 2" faux wood vertical blinds in the master bathroom of my home. The window has an arch at the top, and so the existing blinds were attached down at the "straight" part of the window. Inside mounts were used, with no center support (there is nothing to attach the center support to). The width of the window is 59." I cannot use the existing brackets (a bit too small) and so will install the ones provided with blinds. I had planned to install them the same way as the previous blinds had been installed, but am now wondering if a center support should really be used with blinds this wide. I know I could install a "shelf" across the window and then attached the blinds to this, but the previous blinds did not seem to show any "sag" and so am not sure this is needed.

Just don't use vinyl (very heavy stuff) and only go with aluminum slats and especially a steel header bar (the most important part, for you). If you feel it's still inadequate, you can attach the blinds to Angle Iron. You won't be able to hang from it, but it will be stiff and straight forever.