Once level I used my other sanders to smooth out the whole thing.
To add a bit more insurance, I bought more chain & hooks.
Thanks for reading!
UPDATE: after showing off my chandelier to my brother - who is much better and knowledgeable at household DIY than I am - he was afraid for me, as the ceiling was not meant to support so much weight. This made me scared, so I took down the chandelier and hooks and patched up the holes I made.