It can't. Nothing with mass can get to light speed, everything without mass has to go at exactly light speed, as far as we know.
http://cosmology.berkeley.edu/Education/BHfaq.html
"You can think of the horizon as the place where the escape velocity equals the velocity of light. Outside of the horizon, the escape velocity is less than the speed of light, so if you fire your rockets hard enough, you can give yourself enough energy to get away. But if you find yourself inside the horizon, then no matter how powerful your rockets are, you can't escape."
According to the above, an object must be at the speed of light going into a black-hole, anything less would make escape possible. For something that is at the whim of gravity once that point is reached that's it.
Now say two light emitting objects that have a form of propulsion (say it is capable of 0.75 of light speed) on board, follows that same object, one has it's power (propulsion engines on all the time fighting against gravity) on all the time and the other turns it's power on at a certain point.
The object that has no power on would reach a point where it would no longer be visible, if max power was turned on an instant after it became invisible would it then become visible for even just a moment?
Would the object that has it's power on all the time have a different event horizon than an object that had no power, it's rate of descent would be slower by the amount of propulsion it was capable of.
The above doesn't take into consideration that a galaxy has rotation, so all those points, if they are considered to be equal would need to be at the same relative location to the observer.
From that observation point all matter is swirling around the black-hole as well as heading towards the hole itself. Say matter that is shedding light is moving away on one side (right) and coming towards the observer on the other side (left). Given the same distance from the horizon both should have equal velocity. From the point of the observer the right side should have a higher velocity (observed)because it is moving further away from the observation point. The one on the left should have a lower observed velocity because it is moving closer. Near the speed of light one side could exceed the speed of light because of the added velocity caused my it moving away from the observer. The other side would appear to be moving slower by that same amount. Wouldn't that effect also make it appear that the center of the black-hole is off to one side?
You also mentioned that you cannot see light because gravity has it trapped (rather than the speed of the object). Say your observation point is just a bit above the plane that most of the material is on (like a dinner plate). On the near side you can see the event horizon and then blackness after that point. Say the blackness is 1/4 of the diameter of the plate. Can you see the event horizon on the other side of the black-hole? From a low enough angle of observation (closeness to the plate) so that the other event horizon (straight line of sight) would be less than 1/2 the diameter of the hole. If light is affected by gravity you shouldn't be able to see the other side (light is sucked in), if light is not affected by gravity you should be able to see the other side that is the same distance from the center of the hole as you can on the near side.
The speed of light is the same for all observers all the time, regardless of their state of motion or the state of motion of the light source. If something that's receding from you is accelerating, it'll always be visible, at least in principle, its velocity relative to you will never get to the speed of light. It won't "wink out" on you. Once in sight, always in sight.
Just to make sure you got my general drift I'll get to a very simple explanation, for my benefit not yours.
A person is at point A, a straight goes both left (point B) and right (point C) from there. The line and points are stationary. A person looks from point A towards point B. A light source leaves point A going towards point B at 0.9 light speed. With some optics you zoom in as it moves away from you so it stays the same size in your vision. You should be able to see it forever. The light is traveling back to you from the object at light speed but it is not the same as it was when it was stationary at point A (color shift if nothing else). With neither the observe nor the light source moving it is reaching the observer at light speed (white light). What happens if the observer starts heading towards point C at 0.9 light speed (opposite direction than the light source took off in) The combined speed away from each other is 1.8 light speed. This is where I fail to (pun intended) to see the light. No light is coming from point A the only light on is from the object headed towards point B.
Now time could be introduced, same as my previous example, say there was a marker on the light and the light rotated once/minute by the watch the observer held. Once the lighted object started to move that rotation of the object would not change for the object no matter what change in the speed that was separating the two. But would there be an apparent change in that rotation from the observers POV?
I hate repeating myself I just want to make sure you understand what I'm trying to describe.
I haven't thought your example of the galaxy moving along your line of sight all the way through, but from your perspective clocks in that galaxy will be running more slowly than yours, and since its rotation period provides a kind of clock, I'd expect it would appear to you to be turning more slowly the faster it's moving, in either direction. If it were moving across your line of sight, its shape would also change, appearing to shrink in the direction of motion. It'd take a pretty hefty relative velocity to make such effects noticeable, something over 40,000 km/sec to make a 1% difference in anything you can measure. And since galaxies actually rotate on a scale of one revolution in hundreds of millions of years--our solar system makes one orbit in about 225 million years, so it's made less than 2 dozen orbits in its lifetime--you'd be hard pressed to detect anything at all.
That's why I made the numbers so small. In the link in this post they explain about escape velocity. If that is applied to the big-bang then as soon as initial velocity is achieved (leaves the hand) things should start slowing down. Gravity between celestial bodies should have the same effect. The universe is still accelerating, so we are either the apple that is still in the hand (not released yet) or we have have escaped earth's gravity (slowest velocity) and (if tossed in the direction of the moon) if we are picking up speed then we are being pulled towards something.
For the expansion rate of the universe, what you want is the Hubble Constant. Best current value I think is 71 km/sec per megaparsec if my memory is correct, plus or minus about 4%, which means for every million parsecs of distance from you, the recession velocity of whatever you can see increases by 71 km/sec. A parsec, a contraction of parallax-second, is about 3.26 lightyears. Hold your hand out at arms length and make a thumbs up sign. Look at your thumb with each eye alternately, while the other is closed, and notice how your thumb's position appears to shift against the background. That effect is parallax, and comes from viewing things from different angles, in this case the corners of an equilateral triangle whose base is the distance between your eyes and height is the distance to your thumb. A parsec is the distance at which something will appear to shift against the more distant background by one second of arc in observations made six months apart, from opposite sides of the earth's orbit.
I was hoping to find a number that is in % of a light years from any galaxy that is headed in the opposite direction, I could then divide that by 2 to get how fast our world is heading away from where the big bang took place. Then the rate of acceleration could be applied but that part of the question I was forming isn't necessary
at this early stage. I don't have any mass or distance numbers for any object that might be pulling us towards it.
It would be interesting to know if all parts of our universe (ball form) is accelerating at the same rate. If one portion is accelerating faster than another then an object is more likely to be in that direction.
One last thought, if matter (only thing that can cast it's own light or reflect light from another source) cannot obtain true light speed then is a black-hole truly black? Couldn't a tiny portion escape but it appears black because of the brightness of the light matter is shedding just before the event horizon. If you cup your hands over your eyes and keep your eyes open it will appear black at first, once your eyes become accustomed (say 5 min) it is no longer totally black as it will tend to be a dark blue-gray, for my eyes anyway another person might have a slightly different color depending on if there are any differences in color vision normally.