After having spent many hours searching how to fix this problem of uploading an image (likely large) and only getting a message of HTTP Error the FSD Web Penguin finally figured it out. The solution was dead simple too. Mileage may vary based on your hosting service.
All of the references pointed to some known ImageMagick issue with WP. Finally we looked in to our hosting provider after having tried all the .htaccess and function.php modifications found everywhere. It was clear that the provider offered the ImageMagick PHP extension. We finally read on to find out that the provider DID NOT ENABLE the extensions by default. Likely for security reasons and we can fully understand that.
edit your php.ini to include
extension = imagick.so