Has this ever been tried? The respective aromatic ions are readily accessible, e. g., in the form of sodium cyclopentadienide and tropylium bromide. It shouldn't be hard to just combine these two salts. People have went down much more intricate ways to obtain exotic aromatics. Especially considering the prospect of a pure hydrocarbon ionic compound (maybe even an ionic liquid?), formally derived from benzene by intermolecular exchange of a CH⁺ charged ring segment. Or call it, with some hand-waving, a heterolytic cleavage of azulene.
I've done some superficial peek into literature (tricky, since there are tons of sources discussing the two aromatic ions separately); best I cold find was https://doi.org/10.1248/cpb.11.126 with their compound VII:
(with some bulky substituents on the cyclopentadienide ion), that “easily formed red crystals” from aqueous solution. Apparently, though, learning about the pure C₇H₇C₅H₅ was none of their priority. But the fact that this is isolatable, and doesn't fall apart/rearrange immediately, sounds promising to me.