Hi Brietta -- I'll respond to another point of yours. You asked, what is the evidence for Jane Tanner's memory becoming progressively better.
This was the e-fit she produced after her initial interview. She later said in her rotatory:
"4078 “I know this seems like an obvious question, which I think I know the answer to, because I’ve seen the artist’s impression, did you see the man’s face?”
Reply “No, no, not, no, I mean, just the hair, well not, not that I could remember to give details.”.
Cite: http://www.mccannpjfiles.co.uk/PJ/JANE-TANNER-10MAY.htm
That is entirely consistent with the e-fit she produced at first (below), and even the later e-fit. It also ties in with her initial statement, so all is fine there.

BUT....
If in her initial interview, she was adamant she could not see a face. And if in a later e-fit, she confirmed that she couldn't see the face again... why did she then make a positive ID from a facial pic?

Her memory improved to the extent that she was secretly recorded identifying a man -- from a facial shot -- with the language "that is the man that I saw carrying the child." -- confirmed by Tim-Craig Harvey, who was paid by the McCanns to coordinate the private investigation. A voice analyst, also paid by the McCanns also noted with regard to her memory: 'the more she had to describe him, the more accurate she became.'
Cite: https://www.youtube.com/watch?v=vphKz-Xjbn0 (From 15 minutes exactly to 16.15).
So to sum
May 2007 -- initially after Madeleine was removed from 5A -- no ability to recognise a face.
During the private investigation -- secretly recorded identifying a man as the man she saw via his face.
--
I'll end on this note. Jane Tanner said during her rotatory interview that: "the best thing that could happen to me, apart from Madeleine being found, is somebody coming up and saying ‘That was me’, you know, ‘That was me walking across there." http://www.mccannpjfiles.co.uk/PJ/JANE_TANNER_RIGATORY.htm
Scotland Yard did find that man. He did come forward. Everything about him tied in with Jane said - so she can relax about that now. SY know she didn't obstruct the course of justice or anything like that. Her eye-witness account can now be corroborated, so we should thank her for being so alert that night. They know the child wasn't Madeleine. So Jane simply becomes a witness to the other thing she saw -- Gerry and Jeremy's conversation. Near the gate of 5A.
Jane Tanner was consistent and concise in each witness statement she provided.
The illustration is of the man she saw and the clothes he was wearing ... and as can be gleaned from the rogatory statement, the Portuguese were unable to assist at the time.
... but I think I’d prefer just to stick with what I said in my original statement, in terms of the, because even, I mean, this is coming back to the sketch, even when I did the sketch, by that stage, you know, things were, were murky,I needed to that sketch that first night, I mean, they took me in to do the sketch, but they only had, erm, front facing software, so you know, and at that point I said, you know, is there, can I do,
because the clothes and everything was the thing was the thing that was the most in my mind then and I can remember saying to the chap I met on the stairs earlier, I think it’s (inaudible), is it?”
4078 “Yeah”.
Reply “Because he took me in the car back and forth and
I can remember saying to him on the way back ‘Look, is there a way I can do a sketch with clothes, you know, do you have software or any way that I can do a sketch of the clothes or a side, a side view’. And he sort of said ‘No, we don’t have that feasible, you know, feasibility or availability’. And I said then ‘Can I do that when I go back to the UK’, you know, because at that point it was in my head and it would have been, and they were the bits that I think would have been recognisable to get down on paper. But at that point it was like ‘Oh no, we can’t do that, we don’t work in that way’. Which I can understand and, you know, now obviously I think ‘Oh I should have pushed and really pushed’, but at that point you rely on, you don’t, you know, you’re just in such shock and you just think ‘Okay that’s the way things do’, but”.
4078 “Yeah”.
http://www.mccannpjfiles.co.uk/PJ/JANE_TANNER_RIGATORY.htmI think you are mistaken when you state ... "Her memory improved to the extent that she was secretly recorded identifying a man -- from a facial shot -- with the language "that is the man that I saw carrying the child."
Cite:
https://www.youtube.com/watch?v=vphKz-Xjbn0 (From 15 minutes exactly to 16.15)
I heard a man saying " she was then presented with a photograph of this guy George in a market at which point she broke down and said "that is the guy that I saw carrying the child."
I did not hear Jane Tanner saying it nor have I found confirmation elsewhere that she did although it is possible she may have recognised a profile ... do you have a definite cite as the youtube video definitely won't do.