If I am following the idea correctly, SOAP API would be a viable option.
1. SOAP getMultipleLeads would request all leads based on a specific date and/or field (such as "not conracted yet")
2. A script on the landing page pre-populates the form with the first lead
3. The marketer calls the lead to confirm details
4. When the marketer submits the form, SOAP syncLead updates the theoretical field "not conracted yet", removing the lead from the call queue.