I’m glad to see other people following this line of argument :)
I agree that many true payoff functions are likely to have high-hanging fruits, e.g. any cause area aiming at social change that requires reaching a breaking point would have such a payoff function. 
However, it's expected payoff functions we're interested in, i.e. how we imagine the true payoff function to look like given our current knowledge. I’ve also thought a bit about whether there would "high-hanging fruits" in this sense and haven’t been able to come up with clear examples. So, like Harrison, I would take issue with your second claim that "high-hanging fruits may be prevalent". I cannot think of any cause area/interventions which could plausibly be modelled, given our knowledge, as having high-hanging fruits on a sufficiently large scale (unlike the examples in your footnote 3, which have increasing marginal returns at a very small scale). 
This is because when we take into account our uncertainty, the expected payoff function we end up with is usually devoid of high-hanging fruits even if we think that the true payoff function does have high-hanging fruits. This happens, for example, when we don’t know where the threshold for successful change (or the stairstep in the payoff function) lies. And the less information we have, the less increasing marginal returns our expected payoff function will have.  I think this applies very much to the two possible scenarios you give.
The most promising examples of expected payoff functions with high-hanging fruits I can think of are cause areas  where the threshold for change is known in advance. For example, in elections, we know the required number of votes that will lead to successful change (e.g. passing some law). If we know enough about how the resources put into the cause area convert into votes, our expected payoff function might indeed have high-hanging fruits. (However, in general we might think it would be increasingly harder to "buy" votes, which might imply diminishing marginal returns.)
In any case, I would also be very interested in any convincing real-life example of expected payoff functions with high-hanging fruits. 

I think it’s good to consider these kinds of hypotheticals, and I don’t know if I’ve seen it done very often (although someone may have just expressed similar ideas in different terms). I’m also a big fan of recognizing stairstep functions and the possibility of (locally) increasing marginal utility—although I don’t think I’ve typically labeled those kinds of scenarios as “high-hanging fruits” (which is not to say the label is wrong, I just don’t recall ever thinking of it like that). That being said, I did have a couple thoughts/points of commentary:

• There are a variety of valid reasons to be skeptical of such “high-hanging fruit” and favorable towards “low-hanging fruit”—a point which I think other people would be more qualified to explain, but which relates to e.g., the difficulty of finding reliable evidence that massive increases in effort would have increasing marginal returns (since that may mean it hasn’t been tested at the theorized scale for impact yet), the heuristic of “if it’s so obvious and big , why are we only now hearing about it” (when applicable/within reason of course), the 80-20/power law distribution principle combined with the fact that a decent amount of low-hanging fruit still seems ripe for picking (e.g., low-cost, high-impact health interventions that still have room for funding), and so on.

• I suspect that as the benefits of/need for mass mobilization become fairly obvious, the general public would be more willing to mobilize, making the EA community less uniquely necessary (although this definitely depends on the situation in question).

• The EA community may not be sufficiently (large*coordinated) to overcome the marginal impact barriers.

• Applying the previous points to the scenarios you lay out (which I recognize are not the only possible examples, but it still helps to illustrate): for hypothetical 2, regarding climate change, this seems to be a case where it seems very unlikely that the general public will fail to support such a promising intervention while the EA community would be the unique tipping point to reach massive impact; in hypothetical 1, regarding animal advocacy, such a situation seems fairly unlikely when considering the reasoning behind diminishing marginal returns and historical experience with animal advocacy (e.g., there are going to be people who are difficult to convince), and again it seems unlikely (albeit less unlikely) that EAs would be the unique tipping point for massive impact.

• Especially considering the previous points, I don’t know how widespread/bad the assumptions of diminishing marginal returns in the EA community actually are in practice relative to its inaccuracy. I think it probably is an area for improvement/refinement, but it’s always possible to overcorrect, and I suspect that when/where increasing marginal returns becomes fairly obvious EAs would do a half-decent job of recognizing it (at least relative to how well they would recognize it if they thought about these scenarios more often).

I had similar thoughts , too. My scenario was that at a certain point in the future all technologies that are easy to build will have been discovered and that you need multi-generational projects to develop further technologies. Just to name an example, you can think of a Dyson sphere. If the sun was enclosed by a Dyson sphere, each individual would have a lot more energy available or there would be enough room for many  additional individuals. Obivously you need a lot of money before you get the first non-zero payoff and the potential payoff could be large.

Does this mean that effective altruists should prioritise building a Dyson sphere? There are at least three objections:

1. According to some ethical theories (person-affecting views, certain brands of suffering-focused ethics) it may not be desirable to build a Dyson sphere.
2. It is not clear if it is possible to improve existing technologies piecewisely such that you a obtain a Dyson sphere in the end. Maybe you start with space tourism, then hotels in the orbit, then giant solar plants in space etc. It could even be the case that each intermediate step is profitable such that market forces will lead to a Dyson sphere without the EA movement spending ressources. 
3. If effective altruism becomes too much associated  with speculative ideas, it could be negative for the growth of the movement. 

Please do not misunderstand me. I am very  sympathetic towards your proposal, but the difficulties should not be underestimated and much more research is necessary before you can say with high enough certainty that the EA movement as a whole should prioritise some kind of high-hanging fruit.