I apologize, but you don't understand relativity.
Neither do the people you are quoting.
Heck, I barely understand it, but I believe I understand it well enough to help you understand why your questions don't make sense.
I'm going to make this answer a community wiki. If you are ABSOLUTELY SURE that I've misrepresented or improperly explained something, please feel free to edit and improve this answer.
Time should be discussed in reference to something else. We get away with ignoring the "something else" when we talk about time because we're all experiencing it together — there's no (significant or perceptible) difference in the time experienced between individuals or objects.
Think of it this way: in your high school physics class you should have been introduced to the idea that voltage is a potential difference. There's no such thing as, for example 20 volts DC. What there is, is a difference in potential of 20 volts DC between two reference points — one of which is arbitrarily declared to be zero. Electricity is magic that way. The "actual values" could be 100,020 volts and 100,000 volts, but because only the difference matters, we only care about the 20 volts. (The 100,000 volts would only matter if there was a third reference.)
This shouldn't be surprising. It's like a canal between two oceans. It doesn't matter how large the oceans are, it only matters that there is a difference in altitude between them. If there is a difference, water flows from one to the other. If there is not, the water in the canal is stagnant. I realize that's a metaphor to explain a metaphor to explain a very complex issue, which is what we introduce next.
Time kinda works the same way. Those particles you mentioned in your quote were not "hurled into the future at high speeds." Traveling at (or, fictitiously, beyond) the speed of light is not "time travel" per se. The person on the ship does not experience time in any way other than they always have. The atomic particles disintegrated at exactly the time they were supposed to — from their point of view.
From our point of view, it appeared they did not. That's because the difference in the perspective of time between the traveler and the observer is that the traveler's passage of time slowed down.
The traveler's perspective is that time everywhere else sped up. So, when they walk off the ship, a lot of "local time" has passed.
Is this time travel? Not really. Not in the way Science Fiction has traditionally presented time travel. You didn't walk into a portal and find the future on the other side. And you certainly cannot walk back through the portal to your own time.
Now, let's look at your assumption
I came to the conclusion that if someone wants to make a leap of time, they have to go beyond the speed of light and eliminate their mass. In other words, eliminate their physical form and life.
That isn't how relativity, time, gravity, or anything else works. Remember, you're not actually "time traveling." Your perception of time (or your mass, for that matter) doesn't change. What changes is the perspective between you, the traveler, and someone else (e.g., standing on Earth), the observer. The observer sees changes in the traveler. The traveler sees changes in the observer.
I believe it is a misconception that traveling closer and closer to the speed of light means you are converted into energy. That's not how it works. The fact that a photon of light has no mass (from the perspective of us, the observers) does not mean we become some form of conscious light when we travel at the speed of light.
And they didn't need to travel beyond the speed of light to achieve that time differential. The faster you travel, the greater the differential between observer and traveler. A baseball experiences the same time throughout its existence — but during those moments when it's traveling toward a batter at 100 mph it's experiencing time more slowly than the batter is.
It's nice to think that a baseball's lifespan is lengthened through use. Of course, that's compensated for by the destructive force of the bat....
What if someone or an object is given the opposite of it all? What if someone or object is given the slowest time and the heaviest mass?
And that leads us to this next problem. You don't speed a person up by removing their mass, their apparent mass (compared to the observer) changes as they speed up (compared to the observer). Relativisticly, it is thought that photons have mass. In other words, from the perspective of the photon, it has mass and it never changed.
Which is a lengthy way of saying you can't slow a photon down simply by increasing its mass. Nor will its mass increase if you slow it down — you, the observer, will simply see the mass the photon always had because the effects of relativity are no longer in the way.
That last statement probably caused Einstein to wake up in his grave and start screaming. But, zombie-Einstein remains entrapped in his grave, thank goodness!
What you meant to say was, if the motion of a person slowed down compared to someone here on Earth, it would appear time sped up for them and their mass increased. It didn't, of course, from their perspective (the traveler), but it would appear so from yours (the observer).
Is this time travel? Nope. When the traveler gets done traveling they'll discover less time passed than they thought did, but time passed, nonetheless.
But what does it mean to "slow down?"
That's a darn good question. You can sit as still as you possibly can and you're still traveling due to at least (a) the rotation of the Earth, (b) the orbit of the Earth, (c) the motion of the Sun around the galactic core, (d) the motion of the galaxy as it saunters through space, (e) and who knows what else. And that's ignoring the fact that the atoms in your body are in motion (most notably the electrons spinning around the nuclei). In other words, slowing down is very much more difficult than it sounds...
...because our point of reference is our planet, whose motion is substantially greater than anything we can bodily achieve anywhere but in space, which is why earlier I could say that we all ignore the reference point ("potential difference") when we talk about time one with another. The minor difference in time as we pass one another in the street is statistically irrelevant.
The time differential is not linear
Finally, as people slow down in relation to us, here on Earth, very little happens. They would need to "slow down" a lot. That's because (if I'm remembering this correctly), the changes in the perception of time between traveler and observer is exponential. As the traveler linearly accelerates toward the speed of light, the observer sees time slow down exponentially until the traveler hits the speed of light and the observer thinks time has stopped for the traveler (remember, from the traveler's perspective, nothing has changed. Time is moving along normally.)
Conversely, as the traveler slows down (in relation to the observer) it appears the passage of time is speeding up — but the traveler must slow down A LOT for a perceptible difference to be seen. Theoretically, the traveler eventually hits zero relative speed, at which time the passage of time from the observer's perspective is infinitely fast and the traveler appears to cease to exist. But from the traveler's perspective, time is passing normally and they have an entire lifetime to spend.
Curiously, this is what we think happens when people cross beyond the point of no return toward a black hole. We would see them disappear in the wink of an eye, but the traveler seems to fall into the black hole forever.
Which is why Joe Bloggs brought up the black hole: the "heaviest mass" and the "slowest time." But only from the correct point of view.
What you're asking doesn't make sense. It doesn't make sense because a person's motion doesn't change the fact that they are always moving forward in time and, from their own perspective, always have the same mass. You can speed up or slow down the perception of that passage relative to something, someone, or somewhere else, but that isn't time travel. And changing your speed only hastens or slows your personal lifespan compared to that other person, place, or thing. Is it destructive to slow down? Sure... in the same way that it's destructive to simply live your life. You are born, you live, you die. How quickly you appear to do that in the eyes of an observer depends on both your velocity through spacetime and theirs.