You bring up some really good stuff, I had never heard the Jamison as daddy theory. Could it be, hmmm.....I have always thought it was Lizzie. As you said, strongly implicated in the beginning. And I disagree that she would not be able to hide it. Who would make that so difficult? She had no parents alive at the time, presumably. (Kind of bites the Jamison theory, do we KNOW when her parents died? I thought it longer ago than Vicky's age.)
As heiress, she could pretty well do what she pleased. If she said she was going to Europe on an extended tour, it would have been accepted. And that was not an unlikely choice for a young woman in Lizzie's class and finances. We know Roger was away at school. We don't know of any long term staff other than Matthew Morgan, and he would not have questioned her going away for a while. I would not for a moment think that she hid away and gave birth at Collinwood.
No other scenario works without re-writing or ignoring established facts in the early series.