I have ridden a Specialized Avatar or Alias that was on a demo bicycle once. Can't remember which one it was exactly, but I do remember having a similar feeling to what you describe - like only the very tips of my ischial tuberosities were resting on the saddle and like I was lacking stability front to back. I also had a similar feeling with a Selle Italia saddle (again, can't remember which model exactly) that was very T-shaped with an abrupt change in width back to front.

Personally, I prefer having my weight on the inferior ramus of the ischium, rather than the ischial tuberosity. It's a larger surface so there is less pressure and it feels more stable, and also the forward rotation of the pelvis provides for a better, more relaxed back position. To sit like this, the shape of the saddle is at least as important as its maximal width. Measuring and matching the width of ischial tuberosities works only if you only sit on them. Otherwise, it's back to trial and error.

The article @woodcraft posted gives a good illustration of how I sit on the saddle (I'm probably not tilted quite as far forward, at least not most of the time). I don't use a Selle SMP though, I'm currently on an older Selle San Marco Aspide (version without a hole). It is narrower than what a sit-bone measuring chart would recommend, yet it offers a lot more support to me than a wider but more T-shaped saddle.

As for your problem, I would suggest you don't rush with changing the saddle just yet. It takes some time to find just the right tilt and set back of a new saddle, and, more importantly, just the right way to position yourself on it. If it still doesn't work after 100-200 miles, then it's time to start looking for a new one.