The cigarette butts as evidence of IDI feels incredibly weak to me. A fairly commonly smoked brand turning up in two locations that can, at best, be tenuously linked to the two incidents isn't really evidence of anything, expect that one or more people in the area smoked that brand. Nearly a quarter of adults and approximately a third of young people in the US smoked in 1996, that's a lot of people.
The Gnome-key, assuming it existed in the first place, isn't particularly strong evidence of an intruder either. PR dropping an barely coherent word-salad about it's existence some time later isn't particularly convincing, especially given it's sudden appearance in the narrative ~2 years later when suspicion of RDI was building. Any time potentially exculpatory claims are made by someone under suspicion they should be treated with scepticism until they can be
independently corroborated (i.e. JR wouldn't "count" for corroborating PR nor visa-versa as both were suspected)
But even assuming we take PR's account of it at face value - by her own admission they weren't diligent about returning it after use, had occasion to use it herself and found it not present and she can offer no indication as to whether it was there at the time of the murder or not.
But let's make (another) assumption that the key was indeed present under "Pierre" at that time, an intruder who either knew that's where they kept a spare or successfully guessed the hiding place (not especially difficult, mats, non-fixed ornaments etc near doors are easily checked and common enough hiding places) could have used it to gain entry. But even with those (multiple) assumptions all that does is ascertain that it's
possible - it provides no evidence whatsoever that it actually happened.
On to your theory of the note:
brought a pre-written ransom note and transcribed it onto Patsy's notepad, and faked a rough draft to make it appear it was freestyled, because it was part of the framing of the Ramseys
In your scenario this intruder is motivated to cast suspicion on the Ramseys, so much so that they are willing to go to fairly convoluted lengths to do so - copying a lengthy yet obviously preposterous ransom note on to their note pad, including a faked
draft no less. Presumably with the intent that anyone reading the note (which would normally be a signal of an external actor) would instead take those factors as evidence of the Ramseys guilt. Of course such measures would be unnecessary - you don't need to discredit the note as coming from an intruder if you simply don't leave a note in the first place. This person (per the key-under-Pierre theory of access) has already gained access to the house in such a way that there's no sign of forced entry, there's no dirt or detritus from outside, no finger prints - no real evidence of someone else being present
at all. With the body of their child on the premises and no ransom note there's going to be a veritable avalanche of suspicion falling on the Ramseys anyway. Probably far more so than with the a note of debatable provenance!
Is it impossible? No, and people do all kinds of things that appear to run counter to common sense and rationality all the time. But, as with the Pierre-key above not proving something to be
impossible is not the same thing as evidence that it happened. I'm not someone who puts much likelihood on IDI in the first place - but this doesn't even strike me as the most likely IDI explanation.
