I don't know whether it would work for your child, but you might consider teaching clause analysis and then hanging punctuation on that. For example, putting a comma where there should be a period - or a semi-colon - typically means connecting two main clauses that way. If you understand how to find a finite verb, you have some hope of understanding that.
The other thing I'd do is to point out the arbitrariness of many of the rules; part of the problem may be that he's looking for logic where, really, there is only convention. This is something you notice if you are aware of the differences between e.g. US and British English, for example - we have different rules for how to punctuate speech, among other things.
