I correlate the Kingdom of God with heaven (just like the Bible says). All three concepts — heaven, enlightenment, and nirvana — fit into my belief system quite nicely, and I see no conflict between the three. But I see them as three separate concepts.
The Bible states that the Kingdom of God can be experienced here on earth, I am not sure whether this is compatible with the notion of heaven as everything I have read seems to signify that heaven pertains to the afterlife. Certainly enlightenment and nirvana are conditions which are possible to attain in life.
I would add to that the idea that we retain our individuality, yet we are no longer separate (a paradox).
I would state that we attain individuality, for we find our true core. Prior, we are merely a composite of everything we have encountered, a series of perceptions that we have identified ourselves with and attached to social protocols. Our actions prior to such experience are mostly based on what we feel is expected, after, they are based on what comes natural.
I believe we can still reincarnate after nirvana if we so wish. This is the concept of avataras. And, if so, this says we do not stop ‘existing’ after nirvana.
I would suggest that an avatar is more correctly the reincarnation of a being from the 12th level of existence or higher. There are, however, methods which are supposed to permit it. I do not know the name of it, however it essentially pertains to such deep determination to return that it must be, they then retain the 2nd, 3rd, and 4th bodies which float around the cosmos basically until they can be connected again with a physical body - the 5th body. It is not possible for Buddha to reincarnate himself, however, since this is impossible once you reach the 7th body, but there are occult practices which intend to ready a physical body for the merging. One such method was attempted by the theosophists, they attempted to ready a boy by the name of Natyananda for accepting Buddha. The boy died because it is a very dangerous procedure, the theosophists tried again with his brother Krishnamurti, but this too had quite a negative effect on the man - they were never successful.
I am really not sure why you would want to come back to this plane given the choice, however. Buddha has promised to come re-establish the Dharma due to his own compassion, but I am not sure it is actually possible. It is said that the wheel of the Dharma makes a complete turn every 2500 years and this is as long as these 3 bodies can survive through the momentum of Buddhas determination. The theosophists knew this, but since they were not successful it is probably not possible for Buddha to ever return again now. There are various claims to actually be Meitreya, so perhaps it was not possible for the theosophists because it had already happened. I have not found a claim which has really spoken to me, other than Osho, but his claim comes after his poisoning when he seemed to have become quite irrational.