Is it permissible for me to intend to leave Islam and then re-enter it, in order to start praying anew and be relieved of making up missed prayers, due to the inability to make them up because of suffering from obsessive-compulsive disorder?

These devilish thoughts of apostasy from Islam are impermissible. One must adhere to the religion and cast away these whispers. Intentionally abandoning prayer requires repentance and seeking forgiveness. Ibn Taymiyyah and other scholars hold that one is not required to make up prayers intentionally missed. Rather, it suffices to repent, frequently seek forgiveness, perform supererogatory prayers, and maintain the obligatory ones. This is not considered blameworthy seeking of concessions. We advise striving against these whispers and turning away from them.