If anybody wants to found a startup with me that makes it easier to set up mentorships with tech companies and labs in a way that would somehow benefit the companies as much as it would the students, lets do it.
maybe instead of going after the companies (who might feel the need to get some tangible benefit) you can search linkedin for employees at some of the co's that the 2 students admire. perhaps a person may simply enjoy the benefit of helping someone.