Cornelius Gurlitt, 81 years old and his heart faltering, in early January called a notary to his hospital bed in southern Germany, determined to write a last will and testament inspired by love and hate.

Mr. Gurlitt—stung by the local government’s seizure of the cache of priceless art that he called his life’s only love and by the world-wide furor over the fact that much of it was snatched from Jews by the Nazis—had two desires: to…