I’d actually say that if the aluminum is that thin, it isn’t providing that much stiffening anyway. Esp if the wide face is on the top/bottom instead of left/right. Basically, if it’s a thin strip, it’ll only really add stiffness in the same plane that the strip would lie flat in; another way right describe it, since I’m doing a bad job of it, is that it only adds stiffness in the directions you couldn’t easily bend it by hand.
A 3/8” tube of JB Weld with a steel rod core will be much stiffer than a 1/8” thick strip of aluminum.