I am an ex-engineer and have great respect for the achievements of these people. That does NOT mean that there is a solid "proof" for empiricism. These men made a great many assumptions and then worked through their "proofs" within those assumptions, which are, as all presuppositions, accepted by faith. I am busy losing my butt right now in silver, so I will have to get back with you in more detail on this at a later time. Look for a post from me on this over the weekend if that is ok?
You are clearly confused over the difference between unproved and unprovable presuppositions (some call them "axioms") and empirical methodology.
I would say that my main confusion is with why empiricism is important only when evolution comes up.
When Oppie theorized that you could split the atom and create a nuclear explosion, no one talked about axioms, empiricism, or God.
Yet anytime evolution is brought up, all of a sudden the hard core Genesis literalists come out and tell us that nothing is real, all life and existence is relative, and start assigning very human qualities (like empiricism, spirituality, and purpose) to a very concrete and unemotional universe.