It's true, the dharmakaya does not "die." The Essential Truth is always present, and withstands all sorts of destruction. One Buddha's dharmakaya is another Buddha's dharmakaya. It's all Buddhas dharmakaya. It's even the basis that all the worshiped Infinite Buddhas and Bodhisattva emerge from. It's part of each of us in the sense of the Buddha nature within us.
With your question, does the Buddha exist after he dies, it depends on what you mean by "the Buddha." Does an enlightened being exist after death? As the Master explained, nirvana isn't really "existence." We have to remember that the conventional self never existed at all. The consciousness that moved through samsara is no longer there. But every being is eternally, but perhaps saying we "exist" eternally is deceptive. That's the entire purpose of contemplating the meaning of, "you are the Buddha," or, "the Buddha is within you."
Put simply, if the Buddha is within you, the Buddha exists after death. But the rupakaya does not. In your post you seemed to distinguish the rupakaya from your own body. But the rupakaya is the form body of the Buddha, like your own form. It is the sambhogakaya, or Enjoyment Body, that "exists" for us eternally. But this is not "eternal life." Since the Buddha is not living through the sambhogakaya, he was living through the rupakaya. Indeed, the rupakaya was his life, his birth and form.
The Sambhogakaya actually emanates powerful forms infinitely to help all sentient beings. This includes people, images, anything that can help sentient beings. That's why all Buddhas are seen as one in this Dharmakayic sense. For example, to put this in your own personal terms, if you were to finally become a sammasambuddha (Supremely Enlightened One), you would achieve Nirvana and therefore no continuing to live, and be completely released from samsara, the cycle of death and suffering. However, being suffused into the Dharmakaya (the basic principle of Mahayana), you would be represented by the Sambhogakaya. It is like this: The Dharmakaya can be pictured as the endless atmosphere, and in this atmosphere countless clouds (the Sambhogakayas) emerge, which are basically formed of the atmospheric substance. The cloud body is not living, although it is "real" in the sense that you and I are "real."
In the end, you can say that the Buddha experiences Nirvana eternally, but this "experience" is not anything like samsara, and it's not anything you can picture. It's experience of infinitely pure bliss, no thought, no desire, no clinging to any sort of being. It's impossible to define, as the Buddha explained. It means "to extinguish," and "consciousness without feature, without end, luminous all around." In essence, it is a truly released state of consciousness, utter freedom from karma, from the suffering bound into our hearts. And even in the fundamental school known as Theravada, the heart or mind of an "arahant" (one who has achieved Nirvana) is similar to Nirvana.
"The Sage has declared that earth, water, fire, and wind, long, short, fine and coarse, good and bad, and so on are extinguished in consciousness ... Here long and short, fine and coarse, good and bad, here name and form all stop." Hence, consciousness without feature, without end...
Even the elements of space and consciousness do not remain in what is called "Nirvana." Keep in mind that consciousness as an element isn't the only use of the meaning "consciousness." As so with space. Therefore, the Buddha does not "continue to live" after death. That's the purpose of freedom. Self-salvation from endless living in suffering.
I hope this helped in some way.