I propose we set up a website for an imaginary company claiming to have governments among it's clients. The company would deal with containing and storing whatever the client needs to be stored. We will need a normally looking company portal for it (a few pages like about us, contact info (my best guess is to make the phone number something weird, like when you dial certain numbers you'll only get silence, there are also numbers for monitoring equipment, the data is read out by a synthesizer)). Then we need to put the SCP documents in an obscure catalogue like <thenameofthewebsite>.com/a/old/rm123/ and place them among many different, non-related, not creepy .docs.
WARNING: IF WE ARE TO USE THE .DOC FORMAT, WE NEED TO MAKE SURE THE FILE METADATA IS SOMETHING OFFICIALY LOOKING.
This should work out pretty well.