danb is definitely pointing you in the right direction. The key is indeed to consider how many cycles the system will see at that temperature. The base B31.3 equation with F = 1.0 is intended to give you 7000 cycles.

You should discuss with the client how often they really expect the 500°F case to occur. If it is going to happen once every five years, such that there may be a total of ten times in the life of the unit that this cycle happens, you may be able to work with the client to justify a high stress value that still keeps you below the S-N curve.

You want to avoid having to excessively spaghettify the piping layout with so much flexiblity for a rare case that you end up with stability problems the rest of the time.