Rogo is a stand-alone, open-source assessment system I have seen. I have never used it though.
The idea of using Moodle quiz, via the LTI provider add-on, is also worth pursuing.
Another option is to write some custom code that automatically logs people into Moodle, enrols them in the course, and sends them to the quiz, when they arrive from. However, that is basically what LTI does.