If they really want it to last, have it scanned and printed on vinyl with pigmented inks. Something like an Epson. Then mount to Sintra and cover with the UV plexi. It still won't last forever, no matter what they say about the long life of pigmented inks, but it will last a long time. And then, it can be re-printed and replaced.
Whether paper or vinyl, this is going to be challenging to mount. Unless you have experience, the room and the tools to feel confident, consider subbing this out to a sigh company. They are used to this kind of work and good at it in most cases. (Rick's light-hearted suggestion about a billboard company might actually be an idea worth pursuing. They certainly know how to get posters to survive the elements).
Paper is not going to do well over time in that environment, no matter how you frame it. But it would be good to really seal the frame. Hugh Phibbs has an article on how to seal a frame for high humidity areas. I can't remember where it is, so lets hope he chimes in.
Sometimes I think that customers not only think we are magicians, but are insane. But other times I find out that the crazy thing they are proposing only has to last until their next party. I would have a conversation with them about what they hope and what they expect to happen.
