I have similar tightness/rigidity of the chest symptoms and I use a CPAP. In the process of trying to figure out why. It's combined with back pain from the neck down to the SI joint which is more painful when pressure is applied to the back - like when sleeping.

Working with an ortho doc to try to figure it out, but it may be a neurological issue.

I do the deep breathing exercises as well as try to walk when the weather allows.