Summary: Don't toss the soak water.
First, to address the food safety issue, phytohaemagglutinin is gradually destroyed by temperatures above 175F or so. The FDA has referenced studies (see pp. 254-256) which show that 10 minutes of boiling will completely destroy any of that toxin in beans, though they recommend 30 minutes at boiling temperatures to be on the safe side. Yes, some studies have recommended discarding the soaking water to decrease amounts of toxins before cooking, but there's no need to as long as you are certain to have your beans at or near boiling for at least part of the cooking time.
Also, just to clarify your statement about temperatures near 170F increasing the toxin -- it's true that undercooked beans which never reach higher temperatures will release more of the toxin than raw beans. However, I see nothing so far in the literature that suggests a problem if the beans spend some time at that temperature as long as they spend at least 10 minutes (and preferably 30 minutes) near boiling during the simmering. (As long as your beans are actively simmering for a good portion of the cook time, the toxin should degrade: the real problem comes with slow cookers which never reach a boil or even a decent simmer and might maintain a constant temperature that never rises above 180F to destroy the toxin.)
Finally, I should also note that you've asked about black beans, and the concern with phytohaemagglutinin is greater for red kidney beans and a few other related beans where the concentration is particularly high. Thus there are sometimes recommendations for discarding soaking water for those specific bean types. The concentration is significantly lower in black beans, and while there many be some other lectins in black beans to worry about, as long as they are cooked thoroughly, including boiling for at least 10 minutes, there is no reason to worry.
Regarding your other questions about nutrients, flatulence-causing agents, etc. and the soak water, I quote Harold McGee (who is also referenced in one of your helpful links) from On Food and Cooking (pp. 486-487):
A commonly used method for reducing the gassiness of beans is to boil
them briefly in excess water, let them stand for an hour, then discard
the soaking water and start the cooking with fresh water. This does
leach out most of the water-soluble oligosaccharides--but it also
leaches out significant quantities of water-soluble vitamins,
minerals, simple sugars, and seed-coat pigments: that is, nutrients,
flavor, color, and antioxidants. That's a high price to pay. An
alternative is simple prolonged cooking, which helps by eventually
breaking down much of the oligosaccharides and cell-wall cements into
digestible single sugars.
In line with McGee's recommendations, I generally don't bother soaking at all anymore, since the longer I cook the beans, the more I break down the gas-causing elements. (Also, except in unusual cases, I find soaking -- even long-term -- rarely saves me more than 30-45 minutes of cooking, and for beans I'm going to simmer for a few hours anyway, that doesn't seem to help much.) Regardless, I never discard soak water, since I prefer to preserve the flavor and nutrients.
Some people still find that soaking for a short time will improve final texture or keep beans from bursting or breaking apart or whatever. If you find that it makes a difference for you, soak. But aside from an odd batch here or there, I found that the best textured beans I've made generally have not been soaked at all.
One other minor point is that, while I do sometimes use the oven to cook beans, there's no reason not to simmer them on the stovetop as long as you use a heavy pot. If you're really concerned about toxins, bring them to a boil early (while there's still a lot of liquid), but after 10-30 minutes, you can turn them down to a simmer. Unless you tend to cook beans to the point that they burst and cause the liquid to thicken significantly, you shouldn't need to stir them often (or at all) to avoid sticking.
You can add tomatoes or other mildly acidic ingredients once the beans are near-done, say for the last 30 minutes or so. You're right that you shouldn't add them at the beginning, but adding them a little before the end can allow flavors to permeate the beans more (if you want that). Also, adding small amounts of acid toward the end will actually strengthen the beans somewhat and preserve their structure even if you overcook them a bit.
Otherwise, I agree with basically all of your ideas, which seem well-researched. You'll find similar advice given in many other questions here.
Best Answer
The toxin in kidney beans is destroyed by boiling for around ten minutes, which no doubt holds true for any toxin in the water as well. So there should be no problem with using the soaking water to cook the beans, provided you cook them properly.