My understanding is that open source solution Moodle has a pretty good API.
Per one of my team members who previously worked in higher ed,says "I would recommend Litmos. It is not open source/free but is SCORM compliant and has other bells and whistles like mobile solutions etc. They claim on their website that Litmos can integrate with CRM -- not sure the details"
You of course will still have to create the content outside the LMS, but these solutions would at least manage the students, course enrollments, course progress, etc.