Best way to convince on benefits of a collaboration?

I posted recently about a situation in which I'd made a proposal to build a product for an existing freelance client. An animated discussion ensued regarding NDAs, intellectual property etc. Thanks again for all the advice people shared here on IH, it has turned out to be very handy as part of my negotiations!

Anyway, given the legal situation appears to be less in my client's favour than they first thought, the conversation has shifted. Rather than focus on whether I'm "allowed" to build this product at all, the discussion is now more about me presenting to the client why I would consider it in their commercial interest/benefit for them to collaborate with me building a separate SaaS solution (which I'd then sell to them) rather than them pay me on freelance contract terms to build similar functionality within their existing software.

I have a number of benefits I can put forward that are specific to the product domain/industry, but I'd really value any general advice from IH folk on how to sell the benefits of a collaboration under which they'd essentially be helping steer my development of a SaaS product to sell back to them (I'd own the IP) rather them building it in-house (they'd own the IP).