It's not that being in the present moment slows things down, it's that it switches you to a completely different mode of perception where time does not exist.

When you are focused in the past or future, you are in a mind-based mode of perception, a thought-based mode. This is the mode where the illusion of physical reality appears real and solid to you. Without this mode of perception, you wouldn't be able to play the game of physical life on Earth.

When you are focused in the present moment, you get back in touch with the essence of who you really are. And that non-physical, infinite self is not constrained by the illusion of time so time seems to fade away when you are focused there.

There is more information about this in How do you think less and feel more?

You are also asking how you can remember those "present moments".

Remembering is a mind-based process because it implies linear time cause-and-effect, since you cannot remember things from a mind-based view before they have happened. And trying to use a limited mind-based perception to try to understand "unlimitedness" is not going to give you accurate results because limitation can never fully understand un-limitation.

A friend of mine who had many profound in-the-moment spiritual experiences used to say that the best method he found for dealing with them from a physical reality point of view was simply to leave them alone in that other spiritual reality.

If those experiences were intended to have value at the physical level, the useful parts of them would filter down anyway in a form you would be able to comprehend with your physically-focused mind.

Another point about being in the present moment is that when you are in the present moment, you create less physical time for yourself because when you are in the present moment, you don't need linear time to exist.

So, according to Bashar at least, the more you stay present the more you can have moments where you completely "step out of time". From your perspective, little or no time has elapsed during those periods but from the perspective of others, time has continued to tick at the normal rate.

This basically means you age more slowly than others :)

As the vibrational levels on Earth continue to increase, time is becoming more and more irrelevant anyway. According to the non-physicals, time in 5-D (where we are headed) does not exist in a linear physical fashion. So by the time (excuse the pun) we get there, there will no time at all.

This already appears to be happening as many people are noticing that there appear to be considerably less hours in the day to get things done, and the months and years seem to fly by at an alarming rate.

Some thoughts for you there :)

EDIT

I remembered previously writing an answer relating to the ideas here, and have finally tracked it down: Immortality / Staying Young