Moodle Integration with a PHP project of mine

I've been developing a project using php that my students use to take quizes (that moodle can't do itself) Now I would like to integrate moodle and my project such that my project authenticates against moodle users and reports grades into a courses gradebook. I've so far been authenticating using direct database reading but I'm very hesitant to do writes to the moodle database. I'm also aware of LTI; I am open to using it but the human readable documentation and any samples are impossible to find. If you could provide me a sample or documentation thats less theory and more applicable for LTI it would be greatly appreciated. Thanks in advance.