Your original idea has strength, both literally and figuratively. As you've noted, you have trouble finding a local source, which makes your choice a bit more challenging. You can use ordinary EMT - Electrical Metallic Tubing, commonly used for conduit runs enclosing house wiring. Even 3/4" diameter will have sufficient strength for your purpose, and you can go larger for greater confidence.
Expect the edges of the flattened sections to crack when you squeeze them in a vise. The bends will be 135 degrees, not particularly excessive in this application. You can "step-flatten" the tubing by starting the compression some distance back from the end, turn the vise a few cranks, then pull it out and flatten the next segment a bit nearer the end, until you get the last inch to inch and a half to flatten completely.
Alternatively, you can use any tubing/pipe you can find and create gussets at the intersection. A gusset is usually a flat triangle of material, in your case probably sheet steel, placed along the side of the two pieces to be reinforced and riveted in place. If you have one inch tubing, a four to six inch gusset will be quite strong. Space the rivets about an inch apart, no closer.
Due to the offset between the horizontal and vertical components, you'd want to attach one gusset on the inside of the top portion of the additional tube and to the outside of the bottom portion. If you use the flattened ends method, keeping the flat parts to one side of the tube with a similar orientation should provide a bit more stability.
Another thought appeared in my alleged mind regarding material after searching for some representative images. One can use, for example, a 1"x2" piece of hardwood, such as poplar to accomplish your objective. You would not need a gusset in that case, but here's a picture anyway:
The web site from which the above photo originated provides additional guidelines for creating gussets, most of which would apply only to wood usage:
Railway Bob's Building Tips
If a piece of wood alone does not provide the desired strength, you could yet add a set of gussets cut from 1/4" plywood and have a seriously strong brace.