Great question. I first heard the idea that if there was no god, man would invent one, on a Jethro Tull album cover. But very few people ever ask why that is. Those who do often stop after seeing that the god invention is a way to control people. But still, why? Science minded people understand that we control people with laws because if we don’t, a few will disrupt society for the rest of us. So, we’re pretty quickly at the real question, what is good? And back to the answer that people just give and don’t think about, “whatever god says is good, is good.”
Answering your question, I don’t think it matters what happens to current religions or how logical we become, if we don’t solve our moral problems using logic, then someone will look to the cosmos and make up a higher mind. We came into consciousness after we already developed some of our social skills. We already figured out the Golden Rule before we could write it down. Once we could start thinking about the future, we had already forgotten our past. That past could be conceptualized as a higher mind. We now know it was a mindless evolution but undoing culture is not something you can do overnight.
Your experiment question is slightly different. I don’t believe that if we wiped out all memory of religion, that the Abrahamic God would be rediscovered. Even if we wiped out memories and left the Bible laying around, people would pick it up and interpret it differently than they do now. In a sense, history has done this experiment for us. There is no instance where a god was discovered in one culture that matched another culture unless there was some communication between those two cultures.
** Great story about your 10 year old cousin. I know too many stories of people who didn’t learn about evolution until they were 18 or more. It can be extremely jarring and emotionally difficult to find out you have been lied to all your life. You did that kid a great service, although it probably was not easy for him, better now than later.