Eames Aluminum Group Lounge Chair fix?

I have 2 of the same, have owned them since new in 2000, and one has a wobbly base connection like yours. I looked at the circlip/snap clip on mine and thought it might be possible to find a shim/washer that could fill in the extra space. I have yet to take it apart and try.

The arm connection has always bugged me, not sure if it always used those plastic tube spacers, I doubt it. I think the originals had that spacer cast in the aluminum, which would have been fragile. You should be able to tighten that up, I’d try to take it out in case the hole isn’t drilled and tapped deep enough.