[quote name='Ryuukishi']Well that's a good point. I suspect that the ultimate answer is just that BioWare didn't fully think all this stuff through and indoctrination just works however it needs to work to advance the plot at any given point.

However if I was inclined to fanwank an explanation I would say that the Reaper-based stuff in the Normandy (the IFF system, EDI, the Thanix cannon, etc.) is only BASED ON Reaper designs and knowledge gained from studying Reaper technology; there are no actual physical Reaper artifacts on board.[/QUOTE]
Just to clarify some things:
1) There has never been (and never will be) a case of "instant" indoctrination. Most of the people that were indoctrinated up to that point, had been observing/studying Reaper technology for extended periods of time. In fact, I think the shortest indoctrination was Dr. Chandana's team on the Derelict Reaper. However, it was never stated how long his team was studying the Reaper. For all we know, they could've been studying it for several weeks.
2) Not sure about the IF/F, but I'm pretty sure it's just a simple component. In fact, if you take a good look at it when you acquire it, it kind of looks like the graybox from Kasumi's mission. Best guess is that it's hardware, like a HDD or PSU. Reaper artifacts have always been fairly large (Object Rho, Derelict Reaper, etc.). At the very least, it has to be as big as the orbs you find in Leviathan.
Your assumptions regarding EDI is incorrect. She is neither Reaper tech nor based on Reaper tech. In ME3, it's revealed that EDI (Enhanced Defense Intelligence) was the rogue VI you fought on the Moon in ME1. She went rogue because she became an AI and was confused about what was happening.
However, you're quite correct about the Thanix Cannon. The Codex entry states that it was created based on Sovereign's main weapon (the red laser beams he fires during the Citadel battle in ME1).
Of course, the other thing you have to wonder is how "dead" does a Reaper have to be to stop the indoctrination process? The Derelict Reaper in ME2 was "dead", but looked mostly intact. Sovereign, on the other hand, was blown to bits. Is that dead enough to stop the indoctrination process? Based on what we've seen/been told, I'd say Sovereign was truly dead while the Derelict Reaper was merely in a vegetative state.