First, I don't understand why you don't like Darwin. It's true that his science wasn't as advanced as commonly believed. For example, Darwin believed that if giraffe ancestors had to frequently stretch their necks to get to the acacia leaves, their descendants would evolve longer necks to meet the need. We now know this proposed mechanism to be false. The underlying fact of evolution yet remains.
Capitalism has no easily dated origin.
We can surely say that capitalism began sometime around the era of 1500 to 1800, as you stated. I just don't understand why we need the eonic theory to figure that out. You seem willing to uphold the importance of human agency, or free will, to historical change, mediated of course by circumstances, but it's not clear how this concern is maintained in your eonic conclusions. If it's another predetermination theory, then I guess we should stop trying to do anything purposive and just become hedonists. It seems unlikely.