I'm not going to point by point debate the scenario as it would be, somewhat, pointless as we don't really know what happened.
We do know that after a max of 1:45 of "intense" interrogation, using such techniques as "Remember! Remember who wrote you this text! Why don't you remember? You said you were going to meet someone later, Who? And why is this the first we've heard of it? You said you were with Raffaele all night. Who did you send this text to? Remember!"
I mean, I know that sounds awfully brutal and all, but I just can't see how that would lead Amanda to make a false accusation.
ETA: Really, there's quite a big difference between the responses:
"I don't remember. It might have been Patrick. He told me I didn't have to work that night, so I was just telling him that I would see him later. I didn't mean 'see you later tonight'".
and
"I don't remember. I don't remember. It's him! It's Patrick! He's a bad man" (*not verbatim, but close enough to what she, herself, in her testimony, stated she said).
The prior would not result in the incarceration of an innocent man for 2 weeks. Nor would it have placed Amanda at the scene, as her continued "dream sequence" does. I see no evidence of a coerced confession/accusation here, rather it appears more like Amanda had run out of options and so she attempted to turn the heat off of her and Raffaele, and toward the easiest (at the time) target, Patrick.
To pick up on one point: why do you think that the questioning revolved around who the text had been sent to? The phone was in front of them, and it had the text message and the cellphone number of the recipient on it. Did AK forget (or pretend to forget) who that text message had been sent to? And might Lumumba's number not be stored in her phone address book under his name - making it easy for her or the police to link the number to the name in the event of any "forgetfulness"?
The issue of when Lumumba's name actually came up seems important here. If, as you suggest, the police were still trying to ascertain the identity of the message recipient when AK did her "blurting", then I'd agree that for her to name Lumumba would be odd and fairly incriminating.
However, if it had been established earlier in the interrogation that Lumumba was the recipient (as I currently believe, although if there's firm evidence to the contrary I'm happy to re-think), then it makes more sense that the police formed the logical progression that 1) AK planned to (and in fact DID) meet the recipient of that text message; 2) Lumumba was the recipient of the text; 3) AK and Lumumba met up that night; 4) since AK vehemently denies meeting Lumumba, we can infer that either the purpose of the meeting or the outcome of the meeting were not innocent, and were therefore things that AK wants to hide from us; 5) AK and Lumumba were involved in the murder of Meredith Kercher.
And if the police did follow this chain of thought, it's perfectly feasible that the last section of the interrogation (the last 20 minutes in my fantasy account) homed in strongly on the Lumumba angle.
Also, when you contend that AK's confession was designed to take the heat of her and RS, as well as to stop the police "hassle", why on earth wouldn't she say something like this: "OK, OK, I DID meet Patrick, at the basketball court, as you allege. But we just talked for a few minutes, then he said he was going to visit Meredith, who he fancied. I wondered round the town for a while, and smoked a few spliffs, but I didn't go to the cottage with Patrick". In that way, AK would have subtly redirected the police towards Lumumba (subtly because she wouldn't have actually had to implicate him directly with this explanation), and she would have totally removed herself from the crime scene.
And it's here that a "catch-22"-style problem emerges. If AK was not feeling under pressure, and was therefore capable of thinking relatively clearly, WHY would she place herself right at the heart of the crime scene, as well as implicate an innocent man? If the police were only asking her about the text message, surely AK would have been wily enough to explain that away nebulously ("Oh maybe I did meet him, maybe at the basketball court, but I was stoned. However I'm certain that I didn't go back to the cottage, much less witness or participate in a bloody murder"). It makes no sense.
Or rather, it only makes sense if one contends that AK just totally broke down at this point and gave in to what she'd done. But here's another catch-22: If AK did make the confession because she just couldn't handle the pressure/lies/deception any more, then why did she make a bogus confession that implicated an innocent man? People who "crack" under questioning tend to spill out the whole, unadulterated truth. They don't invent a whole new version of events that's subsequently provably false.
