The problem with your question about the "edge" of the Universe is that there is no edge of the Universe.
An edge, or finite boundary of the Universe cannot exist, for a relatively simple reason. According to the current Hot Big Bang model, prior to the Big Bang, there was no space or time. Not even a void or emptiness.
When the Big Bang occurs, it is not just an explosion of energy; it creates an ever-expanding envelope of space/time (where none existed before) for the energy to exist in. That envelope is the Universe, the matter and energy are just along for the ride.
Let's say we have a hypothetical super whiz bang spacecraft, which is somehow capable of infinite speed. If you jump in and try to drive to the edge of the Universe, you will never get there, because since the space/time envelope is ALL the space and ALL the time that exists, there can be nothing "outside" of it.
No space, no time, no void, not even emptiness.
Due to the infinite curvature of space/time by the mass of the Universe, our hypothetical spacecraft (because it has infinite speed) would arrive where it started.

The relativistic offset for GRO J1655-40 works just fine though, (assuming I don't flub the numbers) because both frames of reference, GRO J1655-40 and Earth are "inside" the Universe.

Regards,
O'Neil