i was going to suggest the same thing but i wasn't sure what was going on with the other end. when i did mine i ended up securing it with 3 screws, but in hindsight it would have been better to have it looped over on a piece of tube as suggested above to allow it self normalise and reduce cupping.
Nice job mate
And best thing is it will roll up smaller than you brush when you are travelling with
I am sure you will have cupping also as mine tries to cup with a full width tube at each end to hold it straight
But either way see how it goes you can always mod it later easy enough