Q. Can you prove that God preserved his word?
A. Many doctrines must be accepted by faith because they cannot be proven. Prove to me that Jesus saves. You can show me in the Bible, but you can't PROVE that your soul has been saved from Hell; you have to trust in Christ that He will do as He promised.
I can show you where God promised to preserve His Word in the Bible, and this is a doctrine, however I can't scientifically prove that He has done so (although there is much circumstantial evidence). I accept it by faith.
You say that because there is no mention of the King James in God's Word, our belief that God has used the King James to preserve His Word in our age is not a Biblical doctrine. I don't believe that God spells out every detail in the Bible. We are told in James 1:2-3 "My brethren, count it all joy when ye fall into divers temptations; Knowing this, that the trying of your faith worketh patience." God doesn't give us the exhaustive list of trails we will face in life, but that doesn't change the doctrine that if we experience trials, it will work patience. If you said, "I'm experiencing a trial that is not listed in the Bible, therefore I don't believe it will produce patience," you would sound immature.
Likewise it's silly to expect that God would have spelled out the names of every version He would use to preserve His Word, but preservation is still a Biblical Doctrine so we can by faith believe that there must be the preserved Word of God available.
I don't understand why you are fighting this so hard, except that maybe you feel you would be looked down upon for accepting this Bible truth at face value. Let me assure you that you may lose some friends, but you will gain others and we all aren't as dumb as we look.