I think this is a great question / thread. I have wanted to learn techniques to accelerate this myself, and clearly there are many people who have similar desires.
The people who have mentioned the stretching - of course we should all be stretching the strings when we install them and after - to get the strings stable. But once strings reach stability, they still often have the zing some of us want to get rid of quicker. And sorry those of you who mention the tone control, but that's only part of the equation. There is no substitute for aged strings as far as getting the zing out - and the comfort that comes from having The Funk on the strings. [look up James Jamerson]
Someone mentioned body lotion. I gotta believe something like that, with the right ingredients, would indeed achieve this quicker, in a safe manner.
I came up with a way recently to mellow the strings out, and they feel Awesome, but I hesitate to share it because I don't know if it is truly safe.
If anyone has Successfully come up with lubes/lotions that have worked well and not killed the fretboard or caused fret lift, do share.