I think that time dilation is a very important factor because it will affect all of your local energy calculations. For example, if you're orbiting a BH at the radius where the rate of time due to gravity induced time dilation is 0.5, you will perceive yourself completing an orbit in half the time that an infinitely distant observer would measure, and thus seem to be traveling twice as fast, which then has implications for your perceived orbital distance i.e. you'd see yourself orbiting more closely. The distant observer, on the other hand, will just see an apparent mass increase and foreshortening.

I don't think that the distance from which the object falls is necessarily the most important factor here, and neither by inference is it's speed. There's nothing to stop us from accelerating, or decelerating the 'falling' object by using a rocket booster or retro thrust. Using retro thrust to slow the falling object would allow the object to be traveling much slower than it's free-fall speed as it approaches the BH, and given sufficient thrust the object could be held stationary above the BH. The length contraction and mass increase factors would then be zero i.e. unchanged, but the gravitational time dilation factor would still be present and would affect your calculations regarding how much fuel you perceive you're burning to maintain your stationary position.

That's an interesting point regarding how a closely orbiting body would see the BH, or rather the EH, as it would have to be orbiting outside the EH. If your local rotation period is equal to the orbital period, so that you're always facing the BH, it, as a point source, wouldn't be appearing to move at all. But then you can't see the BH itself, only the EH, which as you pointed out earlier, isn't an actual surface. However, if you should see other objects falling in to the BH as you orbit around it, you'd see the length contraction and mass effects upon them. Once again though, the events you'd see would appear to happen more quickly because less time has passed for you.

What I'm wondering now is how would relativistic orbital speed time dilation factors combine with gravitational time dilation factors?