but the school seems open to letting him use a computer for a more systematic approach, but I'm not sure what to suggest.
Are they thinking of using a math program like EPGY (now Redbird) or something else?
aeh's advice is right on. Also, this is where you need to know where students in your son's school are...in our DC's school, a 4th grader would typically be VERY solid in multiplication facts (fluent). Remember that MAP is supposed to be untimed. Your DS might not have the luxury of figuring out through addition how to multiply in a higher grade-level class where other students are already fluent in facts (and this could make him stressed or uncomfortable). I would not want to place a child in that math class if they would likely be a weaker member of that class. Students in 3rd grade, on the other hand, are more likely to be learning to become fluent in their multiplication facts.
Another option would be to ask your school..."can we try this for 30 days and revisit, if needed?" That way, if 3rd is too easy for him, you might be able to adjust his level.
The wonderful upside to all of this is that your school is open-minded and flexible!
