If your springs were sized with no CS and there are significant CS effects in the vertical direction around these springs you will have to consider (as you suggest) a few adjustments to your analysis.
Think of it this way, you have the right spring you just have to adjust it's vertical position. Your springs were set with no CS. Picture your springs in place with that last CS gap still open. When you close the gap, the springs may be pulled up or down. Ideally, you would reset the springs by adjusting their vertical position to get everything back to the proper position and hanger load (e.g., by adjusting a turnbuckle). It is this vertical adjustment that you should include in your analysis.
I would run an analysis to see what this delta Y (Y is vertical) is at each hanger point. I would guess that a CS load case, alone, will give you these values. Take these Y displacements and add them as displacement load set on CNodes defined for your hangers. Then, include this displacement set in all analyses performed after the hangers are installed.