How to respond to "what you can bring to our department" in reply of a sabbatical request?
This all sounds like they are interested in you for a reason you don't state and may not know. Laboring alone is difficult, but in some cases it has proved especially beneficial. The case of Srinivasa Ramanujan is instructive. Perhaps you have shown them something in your CV that they haven't considered and might find valuable. A sole researcher will occasionally develop new patterns of thought that are unknown to others. 

But, I think you need to do a bit of research on that department if you haven't already. Who there would you want to work with and why. You need some familiarity with their work. 

You want to extend your range and so do they. If your past results are interesting (to them, primarily) you could offer to conduct a seminar focused on insights for faculty and advanced students. This would be thought valuable. And you could also participate in seminars of other, targeted, faculty. 

But you need to first understand what they do and how what you have done can enhance that in some way. Then, they might be able to overcome the lack of a slot for a visitor.