Alright, first, presuming you can travel at a velocity equal to 100,000*C m/s, which number, btw, is 29,979,245,800,000 m/s, you must consider the effects on the human body of acceerating to such speed. The entire traveling entity, in fact, would be crushed if you tried to use the usual "Jump" to lightspeed style of travel. That makes this hypothetical ship totally impossible.
Now. Had you knowledge of the Law of Gravitation, you would notice that nowhere in the formula is a velocity measurement ergo the speed of the ship doesn't matter for purposes of calulating the Forces involved. Please also note that you state
A force vector of only a single C or less, even if it is experianced, won't lead to a cource change of anywhere near a tenth of a degree, especially because those speeds mean that any outside gravity will only quickly spike and then return to negligable.
which makes abundantly clear that you have not even basic knowledge about which you speak; you just tried to put a force "vector", which I'm pretty sure you don't know what is either, in units of velocity! You can't measure a force in m/s!! Now, look at the Law:
Fg=G*m1*m2/(r^2)
where Fg is the force of gravity, m1 is the first mass, that of your ship, m2 is the second mass, that of the offending body (in your case a black hole), G is the gravitation constant and r is the distance between the two bodies of mass.
This means, for you who need it explained further, that the speed of the ship doesn't affect the force applied to it by the planet. Now, please recall, if you have ever heard of this, that F=ma; that is, the force applied to an object is equivalent to it's mass multiplied by the acceleration it will gain as a consequence of said force acting upon it. So, as your theoretical ship, surely weighing no more than an ocean liner of similar size, say, the Titanic, which massed a mere 41,730,498.04 kg, passes within a lightyear from a smallish black hole with an effective mass of around 10,000,000,000,000,000,000,000,000,000,000 kg, it's safe to say that it will gain some acceleration.
Really, now. The science says that instantaneous FTL transportation is practically impossible and that not having to worry about the masses in the way is even less probable. Too, just for roleplaying reasons, having a perfect instant transportation (not to mention the completely, totally, inarguably impossible FTL communication system you mentioned) is going to be extremely restrictive to the players.
I appeal to your reason. This just doesn't make sense.