As a broker working with quite a few software/SAAS clients, a few insurance companies that I see play well in this space are Chubb, CFC and CNA. They usually offer good terms to software/consulting firms and cover all the bases inherent in third party contracts such as the one you are describing.
If you could use some help on this, consider my hat thrown in the ring.
Our company is just starting out, but we automatically recommend what insurance you should consider based on your business attributes. We can't yet underwrite the policies (still working on that), but at least you'll know what coverage you need (and why).
Just click "build your policy"