Unfortunately for Muslims, Allah never quotes the Injil (or the Torah) even though the Qur’an is all about how respectable those books are. The very first person we have evidence of getting his hands on a Bible went by the name of Ibn-Khazem. He is quoted as follows:
“Since the Quran must be true it must be the conflicting Gospel texts that are false. But Muhammad tells us to respect the Gospel. Therefore, the present text must have been falsified by the Christians after the time of Muhammad.” (circa 1064 AD)
Notice how his line of reasoning is as follows:
The Quran is true
The Bible contradicts the Quran
Muhammad respects the Bible
Therefore the Bible was falsified after the time of Muhammad
This has been proven to be a false premise now that we have undisputable evidence that the Bible has not been changed since the time of Muhammad. Now Muslims must go way back in history and say the falsifications began immediately at Christianity’s infancy. However, this contradicts any evidence of early Christianity as well, making Islam somewhat of a conspiracy theory.
To add to what you said about Muslims changing positions on what the Bible says, I’ll give you an example of something that happened to me. A Muslim once told me that Jesus can’t be God because He says, “My God, my God, why have you forsaken me.” So he literally believed that Jesus said those words. I then mentioned that Jesus said that on the cross, therefore Muslims can’t believe He said it, because Jesus never was on a cross. My Muslim friend quickly changed positions and was able to accept that maybe Jesus never said it, or maybe He said it at a different time.