I guess I was in the same boat, but didn't have to remove the birdcage parts- my chassis came incomplete and didn't have the birdcage. I had to add it. After seeing your pics, I'm starting to think this was a blessing in disguise.
I set the body in place and clamped it, then I bent and tacked the birdcage in place to fit the body as exactly as I could make it. Now I will have the opposite problem you have, I'm not sure how I'm going to get the body off to finish welding all the pieces I've added.
I just wish those guys would stop by and help ME out with their expertise!
Is that a glass body or is it Carbon Fiber? The weave and color look like Carbon fiber like my body.
Keep at it! Let me know if you need any hood and trunk hinges.
Bob