* It's probably too hot there (2000K in the cold part) for fullerene. The atmosphere there is mostly C2, C3 and CO. (CO is mentioned in the paper as a very good guess, but not mentioned in the press release.)
* If you fill a fullerene with H2 or He, it will float less instead of more.
I have a chemistry specification in high school, anyway the conditions are weird. It's like inside a burning coal, but much hotter, 2000K instead of 700K. The density is 2g/ml so it's more like a liquid than a gas. It's far away from the usual conditions in a lab, so my knowledge/intuition are not very useful.
Anyway, at so high pressure and density, I expect molecules with big voids to be crushed.
Indeed, unimaginable what is possible! There will also be traces of H, N, O, S etc due to comets crashing in, so room for carbon chemistry once temperature permits.