You have this partly correctly and partly not.
On the one hand it is said: 'The end of bhava (existence, experience, being, living, becoming) is Nibbana'.
On the other hand Gotama defines bhava as being a product of the indivitual grounded in blindness acting with the intent to create personal experience for himself by way of thought, word and deed.
So what Gotama is saying is that all that is understood to be existence is personal existence.
This is not the way we are acustomed today to think of the idea of existence, but it is necessary to put one's self in this frame of mind to understand how it can be that the goal, Nibbana, can be a consciousness without identification, un-made, but not unconditioned.
Here you need to correct your translation of the three characteristics:
It is not all "experience" anything, it is:
All sankharas are transient
All sankharas are pain
All dhammas (things) are not-self.
The word 'sankhara' has been erroneously translated as 'conditioned' by virtually every translator to date, but this is an incorrect translation. The word means 'con-structed' or 'own-made'.
If you use the awkward translation 'own-made' you will see that what is being spoken of as this consciousness that is not identified with is conditioned, (paccaya), but not (sankharaed). It is conditioned by following the Magga, which results in the elimination of sankharaing, or the creation of a personal world, or what Gotama is referring to as 'experience'.
may all beings be well and happy
and my I act with friendliness towards all living beings
in whatsoever of the 10 directions they may abide,
may I be sympathetic to their pains and sorrows,
empathize with their situations
and be at all times objectively detached