Nope, final cause is the purpose or telos of an object. The end to which it is directed.
That's God.
The issue is, it's not just a method. In principal, it is.
In principle, plumbing is to deal with pipes and flow through them.
But in reality, no method of inquiry can be isolated from the human being who is involved in the process.
Nevertheless, plumbing and science are possible and commonly done. A plumber might be a theist, but that doesn't affect the way he does plumbing. It might affect how he deals with customers, but not how he deals with pipes.
You seem to be working with an idealized version, where the scientist is entirely removed from the picture or there are no underlying philosophies involved.
For example, one atheistic scientist angrily denounced the big bang theory (he coined the term as a pejorative) because it suggested a beginning of the universe. But it didn't have much affect for anyone else.
"If it can't be perfect, then it isn't valid" is a rather obviously false assumption.
There is a great deal of philosophy baked into science that goes beyond the method, most of it coming from a materialist perspective.
Seems unlikely, since the great founders of scientific disciplines like Copernicus, Newton, Darwin, Einstein, etc were believers in God.
When a physicist says "everything is matter" that's an ontological statement
And one no physicist would say. It's wrong on so many levels.
And my issue isn't with science, per se, but with the simplistic idealization of science and the philosophies that get dressed up in scientific garb because their presence in the sciences is treated as non-existent.
There is a philosophy of science. And biologists at least, were once expected to have some grounding in philosophy. But even if a plumber is a theist, he doesn't have to exorcise the demons of blockage to do his work.
Most scientists would be amused by that claim, since most of us are theists or (less commonly) deists of some sort.
Doesn't matter. Notice I said "theists or deists"; many great scientists were deists. Still believers, such as Einstein.
My issue is purely about epistemic hierarchy, because if we are both consistent in our approach and begin with science as the cornerstone of our knowledge base
We would be going beyond what scientists do. What a foolish idea. You might as well make plumbing a cornerstone of your knowledge base.
God becomes rather irrelevant to the world, because He operates with a light touch that makes His presence essentially invisible in nature.
He could have made Himself overtly obvious to all, if he chose to do that. I suppose that He wants each of us to have the freedom to choose Him or not. But He also says this:
Romans 1:20 For since the creation of the world God’s invisible qualities—his eternal power and divine nature—have been clearly seen, being understood from what has been made, so that people are without excuse.
His presence is invisible to science because when He acts by way of miracles such things are by definition not repeatable and immune to testing. Is all this a weakness of science, in and of itself?
It's a limitation of science. It can only work with the physical universe. The supernatural is beyond it's reach.
So even if what you say is true and most scientists are theists, failing to acknowledge the philosophy involved in science(though admittedly it is a stripped down philosophy) is simply playing into the hands of antitheists who seek to use science as a cudgel against religion of any kind.
Perhaps you should consider the difference between ontological materialism and methodological materialism. The plumber doesn't test for demons of blockage, even if he knows there are demons. That's how it works.