You seem to believe that the scientific method and religion are mutually exclusive.
I'm going to split out some terms here. Scientific Method, Academic Science, and Secularism. The latter two are connected to atheism, at least in this era, and are more in line with ideologies and I do not desire to further address or describe them in this post except to say that they do not have a monopoly on the merits of the scientific method.
To speak of the method itself, which is religion agnostic and, as you say, it is a function to provide information as well as the ability to duplicate results. I would append that applying the scientific method to religion works, and that you can, indeed, learn as well as duplicate results through it - as well as reject results that do not work.
A major challenge is that the resultant artifacts aren't readily transferable or inspectable. Many secularists get hung up on this and say it's an invalid application. Essentially that only what the eye can see or the hand can measure is real. I can't really show you my happiness, or peace, or share with you the the depth of experience or knowledge that heals and transforms. I can tell you about it, about how Christ can lead you to peace. I can describe the inputs and results, the complete formula, and then you can walk it and experience the fruits first hand.
Another part of the challenge is that lack of transferability also applies to the instrumentation. I can't provide you a properly calibrated conscience, or the concept of true humility before God like I could a measure of mass or distance. It's all internal to you. Experimentation on that is time consuming and difficult. Some people run experiments with improperly calibrated instrumentation and then fail to get the expected results.