Afaict that's a fairly common approach among those who are willing to make the effort. The need for an easy way to add "omitted" correct answers has already been raised and discussed (years down this forum).
Moodle allows you to add an answer definition "after the fact" and regrade the quiz results so as to adjust the grades. What is left is to find those omitted answers.
Not sure I follow your proposed (or implemented) procedure but it seems that a new engine is somewhat an overkill, especially if this all thing is limited to FIBs. It could be much simpler to construct some means for the students to propose a reassessment of a particular response to a question within a certain time period from completing the test. The professor can review the list, adjust the questions and regrade.
If there are too many cases of omitted correct answers you should probably question the professor's competence. it may be cheaper to replace the professor than to build a new engine and hire an assessor to correct those mistakes.