> What evidence is there to suggest that meaningfulness is a concept that exists outside of our own minds and experience?
Why would you need or want to?
I exist. My mind exists. My consciousness exists. My experience exists.
I mean that in the perfectly ordinary, uncontroversial sense that we use every day. There is no particular mystery or problem when I say, "My cat exists" or "My socks exist". I can provide evidence for them, in the same way I can provide evidence for my own existence and the existence of my experiences. If you can read and understand this post you have evidence for my existence and the existence of my experience.
Furthermore, because we are beings of a particular kind, the things we find meaningful--like the things we find nutritious--fall into a relatively small number of categories. Particulars won't be the same for everyone, but so what? It would be very strange to say that because I like meat and you like fruit there's no objective or universal standard of nutrition, and anyone can eat anything--rocks, trees, nothing--and get along equally well.
Simply because our nature does not determine what we find meaningful or nutritious does not mean it does not constrain it. This is again a perfectly ordinary phenomenon that for some reason people get all confused about when it applies to the contents of our minds rather than the contents of our stomachs.