You can still access the Stability Modifier slider

although it seems to have been restricted from Advanced Part Properties and supposedly only be accessed via XML, it isn't.
All you need to do is enable the good ol' Tinker Panel if you haven't already,, enable "Show Hidden Properties", open Advanced Part Properties, and bam, it's still there.
Here's another crappy screenshot, just in case:

I'm sure this has been discovered before already, but like with my mountain village post (which i still have no clue why it's my most upvoted thing), nobody else bothered to post about it, so here ya go.