Your calculation has no provision for existing cycle damage. Your original post shows how the new cycles lay on top of the existing (damaged) state of the system. Apply this concept to your calculation.

Using your SA equation as your "fatigue curve" (I find (1a) easier to work with than (1b)), you can calculate how many cycles you are allowed. Call that Na1. Divide the current number of cycles used (N1) by this Na1 - this ratio is the amount of total life used (N1/Na1). Now go to your fatigue curve with your new calculated expansion stress range and see how many cycles you are allowed for this reduced stress range (Na2).
Total, accumulated damage is (N1/Na1)+(N2/Na2). Since you can only consume one "life", you can say (N1/Na1)+(N2/Na2)=1. Now solve for N2.