The phrase 'moreover even though' is correct and can be used in written English.
It is used to express that something that is being said is true even though something else has been said or is true. For example, you could say "The restaurant is usually very busy, moreover even though, it was quite empty when we arrived".
Moreover, even though there were occasional scandals that affected the firms, those scandals did not appear to dent reputations or business.
Moreover, even though Evan was the heir apparent, it was not apparent that the top job would be available any time soon -- while he was still relatively young.
Moreover, even though the box was registered in Mr. Bulger's name, Britain has no databank with the names of box owners, Mr. Chase said.
Moreover, even though justices cannot always be counted on to side with the presidents who pick them, chief executives determined to change the court's ideological direction generally succeed.
Moreover, even though he fostered the crusading spirit, he waged war in a less inhumane manner than most of his contemporaries.
Moreover, even though Dell has continued to show better-than-average growth, it has done so by taking market share from its competitors, like Hewlett-Packard, Compaq Computer and Sony, Mr. Kay said.
Moreover, even though the UK economy has recovered since 2012 there is no evidence to suggest that the productivity gap is likely to have narrowed, leaving the UK still staring up the international productivity league table.
Moreover, even though hematology counter device is fast and accurate, it is very costly.
Moreover, even though Fig. 9a indicates the presence of eutectic points, the process was still exothermic.
God is able to know this, moreover, even though the creatures in question will, if created, enjoy libertarian freedom.
Moreover, even though ERs and FPs are designed to be reused, tracking and reusing the ERs and FPs developed by others is practically impossible.
