It's always hard to make such choices, especially in the face of so much uncertainty.
You wrote "If they’re even roughly correct, I’d save several lives if I donated £5,000 to AMF this year. That’s an awe-inspiring ability to have, and seems better than sending that money to the poor households to which GiveDirectly would grant it." I would just point out that bed nets have a good probability of "saving lives," but there's a difference between hypothetical probability and the actual benefits of the bed nets funded by your donation. It's entirely possible, for example, that you could fund thousands of bed nets every year for 5 or 10 years and never save a life: it depends on how many people would have contracted malaria without the nets you funded and out of that number how many of them would have died from the disease. There's a strong probability that you would save some lives, but it's far from certain. According to WHO there were 207 million cases of malaria in 2012, but only 627,000 people (mostly children) died of the disease. I prefer to think that my donations to AMF are sparing some people the misery of malaria, but I doubt I've personally saved any lives.
In contrast, with GiveDirectly you know that your donation is going to benefit the poorest households in some way. Many of those households put the money toward a metal roof, which provides long-term cash-flow benefits (and incidentally also helps reduce malaria risk, since mosquitoes can easily get through thatch roofs). Thatch roofs are expensive and time-consuming to maintain; only certain types of grasses are used for thatch and villagers in Kenya usually have to purchase thatch each year; it's not like they can just go out in the fields and gather it themselves. Many GiveDirectly recipients also buy cows, which also provide a source of income. And overall, there's more data on the benefits of direct cash handouts than there is on any other kind of development intervention.
That said, I'm still giving to AMF, not so much because I believe I'm saving lives but because AMF is such a strong role model for other charities to follow in terms of transparency and accountability.
That's a totally understandable position, and yet it starts looking like "paralysis by analysis." Given all the uncertainties, do you honestly think that in 10 years' time the choice of which charity(ies) to fund will be significantly clearer than it is today? I have my doubts. There will always be the possibility that there's some as-yet undiscovered opportunity that's better than the ones available. You could almost turn this sentence from your post: "It’s very easy to do things and not learn about them and end up spinning in circles, especially with theoretical work." into this sentence: "It's very easy to learn about things and not do anything, and end up spinning in circles, especially with theoretical work."
There are parallels here with other fields where evidence is incomplete, contradictory, and difficult to obtain. For example, in the field of human diet there are strong factions arguing that the optimal diet is a paleo diet, a low-carbohydrate diet, a high-carb/low fat diet, and a few dozen other varieties of diets. Each diet has evidence to back it up, and each diet has been shown to be effective, at least in the short term, for promoting health and avoiding obesity. But none of the evidence is conclusive, and there is a lot of contradictory evidence for each diet. In a case like this, you can't say "I don't know what the best diet is, therefore I won't eat anything until the picture is clearer," because you'd die of starvation several decades before the answers become clear. Instead, you pick a diet that to you seems to have the strongest weight of evidence (or the strongest intuitive arguments in favour of it), and follow it, recognising that you're taking a risk and that time could end up proving you wrong.
I think the cost of not donating now is that real people whose lives could be helped by your donations are not getting that aid. Yes, you might be able to help even more people in the future if you wait to donate to a more optimal charity, but the optimal charity can never be chosen with 100% certainty and you could spend the rest of your life waiting for the right moment when you feel confident enough that your're doing the most possible good.
I'm probably painting this much more extremely than you're viewing it, but I'm sceptical that there will ever be universal agreement on the "best" causes or the "best" charities, and at some point you may want to embrace imperfection and perhaps settle for not literally doing the most good but the most good given the information currently available.
Oh, no, I'm definitely not making that argument. Most decisions have to be made in the face of some uncertainty (uncertainty is a key element of risk: without uncertainty there is no risk and thus no decision to make). I was arguing that we shouldn't jump to the comfortable conclusion that we've saved lives by giving to organisation X based on some statistical probability. And if you evaluate both of your charity choices with that caveat in mind, the differences might be less clear.
Effective altruism focuses on doing the most good with your donation, but there can be a disconnect between the most hypothetical good and the most actual good that gets done with your donation in the end. I don't think this should affect decision making, but I do think it should affect our confidence in how much good we may actually have done. Tom wrote in his post "If they’re even roughly correct, I’d save several lives if I donated £5,000 to AMF this year." I was just pointing out that it would be more accurate to say "I might save several lives" or "there's a strong statistical probability that I could save several lives" rather than "I would save several lives," because that sense of certainty seemed to play a role in his decision.