For anyone wondering about the Madison Li angle, here is a full explanation...
Whilst researching this theory, I have tried to view every aspect from a broader perspective, in order to encompass elements of Fallout 3 (and other games) in ways that make sense.
The idea is that Madison Li was born and raised inside the Institute, having come from one of the original bloodlines. Or at least that's what she believes. In reality, which would actually fit the premise a lot better, she may have been 'found' as a very young child by a scouting party from the Institute and made to believe she was actually born there. This would be very similar to the way that I have suggested Shaun was deceived. If this second option is true, then she could even have been found https://www.google.co.uk/maps/place/Madison+County,+VA,+USA/@38.4286389,-78.2677876,9z/data=http://forums.bethsoft.com/topic/1528436-the-mother-of-all-theories/!4m2!3m1!1s0x89b43fa2d4f1e049:0x72bbc41d577e4788, which would explain her name, as well as her'connection' to the Capital Wasteland. (Note that this second option would actually make the Memory Den highly relevant to Dr Li, and not just Shaun as I have suggested http://www.gamesas.com/topic/1527024-jack-and-nora/?p=24160144).
When she reaches advlthood, bearing in mind she would be totally indoctrinated into whatever beliefs and values the Institute represent, she is sent to the Capital Wasteland. Here, using knowledge acquired at what would most likely be the most advanced scientific facility on earth, she establishes herself within the local scientific community. Her mission? To acquire knowledge, resources, and technology for use by the Institute in conjunction with whatever agenda or plans they are currently undertaking. Note that the information I am suggesting here would effectively make the Institute the https://en.wikipedia.org/wiki/Keyser_S%C3%B6ze of the wastelands.
Being of extremely high intelligence, Li would very easily be able to play a role that would 'prove' to others what a good, kind-hearted individual she is, and how much she values the needs of the many. This would also allow her to be accepted into the community to such an extent, that she would eventually be granted access into the impenetrable fortress that is the Citadel. At the same time however, we must consider Dr Zimmer as part of this equation. There are a number of options here. Either Zimmer had never actually met Li prior to his arrival at the Capital Wasteland, or he was 'in on the act'. Or he may have even had certain memories removed or suppressed.
Looking now at Harkness. Perhaps he had information or data in his 'memory banks' that could have caused a problem for the Institute if it were to get out. Especially if this information related to a hostile takeover of not just the Commonwealth, but the entire East Coast and beyond. This would explain not only why Zimmer was so eager to recover his 'lost tech', but also why Li could not under any circumstances be seen as being involved. It would also give further reason why Li could have murdered Catherine, especially if she was close to uncovering information that could potentially affect countless thousands of post-war survivors.
But why, you might ask, would the Institute be interested in taking over the Commonwealth, never mind anything beyond? Because maybe, just maybe, they are nothing like the 'mustache-twirling villains' that they have presented themselves as being. I actually believe, based on all of my existing research, that the Institute are in-fact scavengers, reborn into a post-nuclear world just like everybody else, fighting for their own survival. And that they not only stole pre-war technology, such as the GECK and the nuclear reactor cores I mentioned in the OP, but also people, including Shaun and Dr Li herself. This would actually fit perfectly with the world of Fallout 4, in which everything we find now has value.
And so, in a bizarre twist that would make them seem a lot closer to many of the other factions in the wastelands, including the Brotherhood of Steel, they scour the wastes, looking for people, technology, and anything else that will ensure their long-term survival. And with their latest plan underway, which would guarantee their access to any resources they would require for the forseeable future, to paraphrase a popular saying, ships are about to get real...