I’ve built more than a dozen websites with Elementor (using their Hello theme), and until I installed your plugin, I never once experienced a double nav menu problem.
As I previously stated, the menu only shows up twice when your QuadMenu is used in the header instead of Elementor’s default nav menu. If I delete your menu, and add Elementor’s own menu back to the header template, the double menu issue goes away. Based on this finding, seems to me it’s the QuadMenu module for Elementor that is broken somehow, and does not play well with Elementor’s own Hello theme.
Perhaps the Elementor team corrected the issue you describe here: https://quadmenu.com/documentation/integration/elementor/, so that now your module is actually adding a second instance of the menu?