Is missing the Fajr prayer and performing it after its prescribed time due to obsessive-compulsive disorder—knowing that part of the disorder is involuntary and the other part can be overcome—considered major shirk that expels one from the fold of Islam?

We advise you to be diligent in waking up early to catch the congregational prayer, by setting an alarm or appointing someone to wake you. Missing the prayer due to your negligence exposes you to a grave sin. What you mentioned is not shirk (associating partners with God), but your negligence in taking the necessary means leads you to the sin of intentionally abandoning prayer. Strive to treat intrusive thoughts by ignoring them and not paying attention to them. You may also consult doctors.