"Yet too many economists believe their quantitative tools and theoretical lenses are the only ones that count as “scientific,” ..."
Economist want to believe that economics is "scientific", while is clearly not, and you keep hinting that they are "relying on quantitative analysis as prescribed by the scientific method".
While qualitative analysis can be considered empirical, it's not something often seen when money is concerned and the stakes are high. Most often you will see papers relying on qualitative methods in the "soft sciences" such as social science. Not to mention "verbal theorizing".. this is the kind of stuff that gets laughed out of real conversations.
I would also suggest you look up what you call ”the scientific method”, it’s a misconception that there is one abstract scientific method to apply to all fields of research. The process of science necesserally differ between formal, natural and social science.
I personally like to summarize economics as ”the art of pretending that sociology (social science) is physics (natural science), by abusing math (formal science).”