Cold spring does not change stress range. Stress range is used in evaluating the effects of fatigue.
Here you are trying to include cold spring in the sustained loads used to evaluate collapse (sustained stress).
Your cold spring is a (self-limiting stress) caused by strain and the Code offers no evaluation of this load in combination with collapse loads. While you may have some reason for evaluating the state of stress in an operating position, the Code does not. In fact, because of Code indexing of stress (the SIF), I would have no reason to expect a Code calculation (and then, a CAESAR II calculation) of stress to match any stress value collected from the field.
Engineers can expect some correlation between field measurements and CAESAR II calculations for loads and displacements as long as there is no shakedown. But when it comes to stress, the Code has its own "reality" to ensure safe piping systems. Follow the rules and no one gets hurt.

Regarding your quotation from the technical reference...
I'm not sure of your reference or if it is current. CAESAR II used to activate cold spring with the (at the time) single force set - F. For many years now, cold spring is activated with the CS as you show it above in load case 6.