I suppose having created the post, it's only fair that I share my own experiences with this kind of intuitive transcendence. The way I experience this most often is thru art. That a'ha moment when the art just grabs me by the throat. It's then that I realize...I am that. I am the very radience and energy that is speaking to me thru the art. Happens when I look at the stars too.
The other experience I want to mention is something I have only witnessed as I am sure all of you have at some time in your life. Or at least have heard of a similar story. I once saw a man jump off a boat into an alligator infested river to save an elderly man who had fallen overboard. When the old man hit the water 6 or seven gators along the shore immediately entered the water and made a B line for the old man. The man that jumped in to save the old man was a regular guy. Just happened to be on the tour with his wife and daughter. This guy didn't go to save the old man because he wanted to, or because it was his duty. He suddenly had an impulse to save the old man. With total disregard to the most powerful law of nature...self preservation he suddenly experienced another set of laws that caused him to jump into gator filled water to save a stranger in peril. Schopenhauer would say this is because he and the old man are one. This is a metaphysical realization transcendent of time and space. It is the realization that separateness is secondary and that the separateness is a function of the experience within time and space. So he was able to transcend time and space and become one with the other. Schopenhauer talks about this in depth in his paper called Foundations of morality. It's an easy read.
One last thing I need to tell you... both men were killed by alligators that day.
Only kidding.....just the old man got eaten.

Yes, but I think intuitive is not a correct word for it. Meditation (no thoughts) with eyes open, especially observing nature without thought becomes attention, pure attention. A couple of quotes that refer to this follows:

“If the doors of perception were cleansed, every thing would appear to man as it is, Infinite. For man has closed himself up, till he sees all things thro' narrow chinks of his cavern.”

― William Blake, The Marriage of Heaven and Hell

A Clear And Quiet Mind Can See The Eternal - Jiddu Krishnamurti

You mean like have a good time no matter where you are? I’ve heard that before. Yup. ?

I'm not even sure what that would look like :0

Yes, time and space are not essential in the mind, in fact neither exists inside the mind.

Yes. Many times I've gone to a place for the first time and it feels like I've been there before.

Yes take some good acid

Our experiences of time vary considerably according to our perception of time in any given moment. There is clock time and psychological time. For something to "disregard" space it would have to be non-spatial and even that seems impossible to imagine. Were it possible to have such as experience that you mention above and other than mentioning it what could be said about it?
I have heard people say that in meditation their experience of time slowed down or stopped. People who had a close call with death say that time froze but these experiences occured within space because without one how can you reference the other?

I have some experiences of memory that give me the impression that some things (everything?)--rather than having "happened"--are happening all the time. I can recollect some things so strongly, intensely, vividly, that I feel like I'm having the experience all over again.

When I reflect on theories of multiple/infinite universes and current understanding of the nature of spacetime, my experience of memory seems uncannily congruent.

Not sure if that's what you meant by "intuitive experience"...

Deep meditation?