Sounds like you're talking about what we refer to as T-shaped saddles vs. pear or wedge-shaped ones.

If the sides of the saddle are forcing you forward so that you're not sitting on the widest part, you need one that's more T-shaped (i.e. has a sharper transition).

Specialized saddles are some of the most T-shaped moderately priced saddles out there. Their Lithia, Jett and Ruby (listed from squishiest to firmest) come as wide as 155 mm, which might be wide enough for you.

I have an old 155 Lithia I could send you to try... the gel padding is completely worn out and I can almost guarantee that because of that, the cut-out won't work for you, but at least you might be able to figure out whether the width and shape are close enough to try a new one?