Problem
We inherited (parts of) a brass bedframe from my spouse's grandparents. We bought a new mattress which came with a modern bedframe of metal rails. The brass headboard has two 6.5' bedposts that connect to the frame and the headboard. The footposts, though, are freestanding. The overall structure looks like this picture although ours is nowhere near as fancy:
See how those super tall footposts aren't connect to each other at all once they get above the bedframe? Now imagine the bedframe is much weaker than the posts and children are swing around pretending to be ninjas. I need to reinforce the frame. Right now, with the posts attached, I can apply a small force at the top and easily distort the frame.
In that GIF, the threaded feet are holding the frame up so it was easier to attach the post. In use, the post would be heavy on the ground - mostly under its own weight - which would offer slightly more resistance than what is shown. However, I think it'd still be fairly easy to rotate the post all the way to horizontal and destroy the frame if I tried. It's a very long moment arm.
Proposed Solution
I was thinking I could add angle iron that runs between the posts and the vertical bolted to the frame and post.
Question
Is this likely to be strong enough? Will it just tear up both sides at once? Is there a better solution? I have MIG welded in the past but I don't have a welder handy. If welding something to reinforce the frame is really the best / only option, I can probably find or rent one. Bolting things is no problem.
I don't know if the bedposts are antiques but the grandparents had them for 50+ years so it's unlikely I'll be able to find replacements if I mess them up. If the solution is to get a new bed frame, we just won't put the footposts up.