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After just dealing with this problem, there's enough improvement here to warrant a new answer:
scene->clearSelection(); // Selections would also render to the file
scene->setSceneRect(scene->itemsBoundingRect()); // Re-shrink the scene to it's bounding contents
QImage image(scene->sceneRect().size().toSize(), QImage::Format_ARGB32); // Create the image with the exact size of the shrunk scene
image.fill(Qt::transparent); // Start all pixels transparent
QPainter painter(&image);
scene->render(&painter);
image.save("file_name.png");