I agree with Michael, those "sprung" restraints should be changed into displacements where you define your measured displacements (e.g., a horizontal displacement to the edge of the pad and a vertical displacement up the pad thickness). Adding gaps to your +Y supports will not give you what you want. Those displacements will carry load just like restraints and the restraint report will show the load at these points that prevent the system from returning to is regular operating position.
Michael's second two bullets will give you an estimate of the loads when you cool down the piping. If I recall, you wanted to know the current set of operating loads. For that you can just use your original model with displacements replacing the appropriate restraints with maybe a few more displacements for any "new" sprung positions.
If your model results "match" what you currently see in the field, you should have high confidence that your model is performing appropriately.