Richards said:
1. The trinary system is spewing "black hole radiation" for half a light year or so in all directions.
It was spewing radiation to a great distance in only three directions. The last direction wasn't as extensive. Tapal even states this towards the end of the episode.
Richards said:
2. The Enterprise is approaching the trinary system under impulse power.
It's generally a bad idea to navigate near a black hole at warp, especially since the navigation systems of the day didn't auto-correct your course because of obstacles and/or dangers.
Richards said:
3. If they turn back now, it'll take two days or so to escape the area of effect.
It's a big area. If they go through it, it will take less time, but this brings me to the next point...
Richards said:
4. There's a radiation-free zone between the three stars.
That's because the radiation wasn't spread out evenly (also, see first answer). Our own sun doesn't even emit radiation in a perfert circle. Solar winds can interfere with it.
Richards said:
5. If the Enterprise weaves its way through the debris and goes between the three stars, they'll be clear in 17 minutes (apparently because they can go to warp once past the three stars).
No. They would clear the area in 17 minutes because they were already deep into the field, and the field did not extend equally in all directions. Tapal even stated this to Archer (also, see first answer).
Richards said:
Nope. I payed attention.
Seriously though, I do remember that in TNG, they avoided black holes like the plague because Enterprise wasn't capable of escaping gravity wells at all. Not even by a long shot. Voyager, on the other hand, was a more advanced ship, and actually managed to escape a black hole, though it nearly destroyed their ship, and IIRC, they were making repairs for at least a few episodes (well, ok, they were always making repairs

).