But we do have a reference point, the atoms themselves. Our problem in understanding has been that we see this in the perspective of time, while the subject is of the particles that are moving. See, the closer you travel to the speed of light the slower your atoms age in relation to other atoms that are stationary, this we understand and has been proven with atoms clocks in real-life (atomic clocks being measured off energy pulses from atoms, which is universal and unchanging)..this being said, lets solve some problems.
No, you wouldn't ever see yourself (or grandfathers you may accidentally kill) because you never go back in time. Correctly, you are moving SLOWER through time. As stated n the original text, you cant ever go further back in time than your point of origin. There only seems to be a relative disparity in past/present/future when you have arrived back to where you were. Furthering this, as you accelerate, you accelerate the time dilation effect, and as you decelerate the opposite happens. There is no sudden shift in time.
So, with all this, we can say with certainty that you wouldn't occupy the same space as yourself. This would imply a staggering effect in space, where you would be in two places at once, which happen to be overlapping. By logic, we are time traveling, affected by space traveling within normal bounds of physics, not 'teleporting' which would be a travel through space while time remains constant, so no overlap would happen (just the same as, say, if you were to move your hand (theoretically) fast enough there is a 'blur' of where your hand was after you moved it. simply, that's not how space works). The act of traveling at the faster speed is the "switch" you would need to turn on 'time travel' mode.
Lastly, anyone moving at the speed you are at is also traveling time at the same speed...because the aging is only relativistic, someone going the same speed as you would be aging the same rate as you are. Doesn't matter in what direction, with you against you, doesn't matter because it is the same speed, and the only way to know if you would be aging faster or slower is to compare yourself to someone who is moving at a different rate. If you would to travel with a companion at near-light speed, both you and your companion would age at the same rate. then his side of the cabin detaches and you two are traveling side by side at NLS, same age rate (the distance in between you doesn't affect aging) then he turns his craft and heads in another direction, since the distance doesn't matter and you both are traveling at the same speed, you both are aging the same in reference to the point of origin(and to each other, same speed so you're practically standing still).
disclaimer time: im not a physicist, and have only looked up facts as needed/wanted, but the relativity theory and time travel have fascinated me for a long time and this is a subject that i have thought through many many many times before. theory crafting, logic, and a bit of evidence is all i have and if there's a flaw in my thought line please point it out. I hope this helps in your writing ;D
(ps, wrote late at night/early in morning so my apologies for grammar and spelling mistakes)