Either using super secure straps or putting heavy things on the lid will work fine.
The binder clips don't do diddly squat once your snake is a little bigger though. They can push those out very easily, so having or not having them doesn't make a difference.
I didn't use the bungee cords like you're using, but I had only used binder clips at one point until my dumeril's boa was just gone one day. The lid handles were still on, and only one side of the binder clips had popped off, meaning she pushed the lid up and squeezed through the edge. (Thankfully I found her soon after in the bathroom!)