Is the intention to fast six days of Shawwal valid if a person intends, deep within himself, to compensate for any defect in the Ramadan fast due to obsessive-compulsive disorder?

You must continue to strive against your ego to repel the waswas (obsessive whispers) and not surrender to them. Your fasting in Ramadan is sound and acceptable, Allah willing, as long as you performed it properly and did not commit any acts that invalidate the fast. There is no justification for distress or depression. The pleasure of Allah is achieved by turning away from waswas, because giving in to them is following the footsteps of Satan, and it brings distress and corrupts one's religion and worldly life. So, be at ease and trust that Allah does not burden a soul beyond its capacity. As for your fasting of the six days of Shawwal, it is valid, and pay no attention to the waswas that assailed you concerning the intention; rather, it is obligatory to completely disregard them.