Pierce Brosnan’s what?!I don't know!
I'm looking forward to learning why not. I prefer Pierce Brosnan's. That's because I would say 'I'm a great fan of yours', not 'A great fan of you'. I can't think why a proper name would change that pattern, unless it's idiom.
Your rewording (italicised, emboldened and underlined above in green) seems like a perfect rephrasing! That is, in my opinion, the best of the lot.I think it's standard to just use someone's name to say you're a fan. So I'd plump for I'm a fan of Pierce Brosnan = I'm a Pierce Brosnan fan.