If you have a Parker store nearby, they'll likely have a stock of stainless steel instrument tubing. You'll probably need to buy a 10' stick.
Another alternative is an online outfit called Small Parts. They now sell thru Amazon. I think they sell in various lengths.I bought a 6' length of 1/2" OD from them a number of years ago to lengthen a towel bar. That was before they went to Amazon.
FYI, the originals were solid plain steel round bar. You'd probably have to apply some heat to flatten the ends of that. The tubing is a good idea, and probably stiff enough to do the trick.
