We have the same problem with our chandelier.. It looks like the cable needs to be shifted to the left- to the negative space between the two rings, but it is the thick wire creating that space.

We've learned to live with it. You could try adding dress weights to the part of the chandelier that swings higher. I'm not sure if there is an inconspicuous place where you could add it to your chandelier.....

https://www.bedbathandbeyond.com/store/product/4-pack-drapery-weights-in-white/1044995089?skuId=44995089&&mrkgcl=609&mrkgadid=3249758710&rkg_id=0&enginename=google&mcid=PS_googlepla_nonbrand_homedecor_online&product_id=44995089&adtype=pla&product_channel=online&adpos=1o5&creative=228386821912&device=t&matchtype=&network=g&gclid=Cj0KCQjwnpXmBRDUARIsAEo71tS1Yq2NQtfwRdvzmQ0RHPHqCtEfShRvkPnU2jU9_PS4RGPwWMvdV40aAhD0EALw_wcB&gclsrc=aw.ds

I know you want a non-weight solution, but other than rewiring, removing those two links and putting a tube for the wire to thread through, not sure what else you could do.

I might buy a bag of small magnets and attach them at the top of the bar that sits high, or even on the inside area above the beads (you might have to paint them to match the frame

That wire needs a bit more slack. Do you know how to install/remove a light fixture? I'm lucky that my father taught me how and I would be able to fix that chandelier ... as long as it isn't huge/heavy and the ceiling isn't over 12ft, then I pay an electrician!

It appears that the rings closest to the crosspiece thread onto a nipple the extends through the crosspiece. There are also nuts between these rings and the crosspiece. I would loosen the rings and nuts to see if you can pull more of the wire below the crosspiece so that the rings, not the wire, are suspending the lower portion of the lamp. If that works and you then don't have enough wire above the crosspiece, look inside the canopy to see if there is extra wire there. If not, you could remove a ring from the chain above the crosspiece to release the tension on the wire.