I agree with your comment that 'An experienced UX person is going to want to come in before requirements'. This is especially true for pure software products.
For some things, though, the software is only a gateway into a wider thing. So for requirements, I wasn't thinking of a list of features, but more like requirements for the outcomes: 'When a customer visits the AirBnB site, they should be able to find and book somewhere to stay within 5 minutes'.
Do you think it's OK to bring in UX even when some of those requirements have been drafted (though not set in stone)? Or do you think that would put off someone great, who wants to start from the problem definition rather than partial solution?
EDIT: When I described my problem to friend, he suggested that what I actually wanted is someone who might describe themselves as a 'product designer'. What are the job title(s) that would resonate best with people who do the type of work you described in your comment?