For a part that big (mass) you'll need a very large soldering iron to get the metal hot enough to allow a good bond for solder. Large irons don't lend we to small parts, so this is therefore probably a job for a torch. However, with either solder or brazing rod, you'll have to set up a jig to hold the flanges to the tube while you're heating it because this job will have to be done in one go, or, as you say, if you try one joint at a time, the others will slip off.
One alternative is a micro-torch, which has a small, hot flame, but you have to be quick before the heat gets to the other flanges. And, they're not cheap and work best on a hot fuel like oxy-acetylene. Even with a micro-torch, I'd set up a jig.
Nice sketch, and I which I were working on such a large scale.