Yes -- the best way to fix this is to never load any scenes. Make your entire Godot game a single scene, and load all of your assets/scenes up front. This is the approach I took for my submission "Frog Finder", to work within the limitations of Godot and HTML5.
An alternative approach to fixing this is to fade out/fade in your audio during scene transitions or when you need to load new resources. This is better for bigger games where you need to load large levels or where it's infeasible to have the entire game in a single scene.
It is frustrating :(