So is the saddle a Specialized Jett?

http://www.specialized.com/us/en/bc/...4&menuItemId=0

Do you know the width, and the width of your sit bones?

Also, another thing to consider is the fore/aft position of the saddle. I'm currently using a Bontrager Affiity. It is pretty comfortable for me. However, I was having some pain on the right side (front edge of sit bone) that I think was due to leftover soreness from trying out a previous saddle that was too hard and also turned out to be slightly crooked. I recently tried moving the Affinity saddle forward by about .5 centimeter, which helped with the sit bone pain but instead caused soreness like you are describing.

So if you haven't already experimented with moving your saddle back a few millimeters, that would be another adjustment to try, just to make sure you're not sitting to far back on it.