The only way to sell that to BK attorneys is to pick up the phones.
Sign them on for free and charge them $XX for every qualified lead that goes through the system. Or charge them $49/month just to use your system on their site regardless of the leads that go through (I prefer this one).
I wouldn't suggest taking affiliated leads, it doesn't make sense for your business model. Unless your wizard can enable someone to file mostly online to where the Lawyer expects significantly less money for the deal, you will have a hard time carving a place for your service in terms of the $$.