It would probably help (me, at least) if you were a bit more specific about what ethical system you're using. 

Some of your post seems like it's using a harmed/not-harmed dichotomy (which doesn't seem like a very useful metric to me, but might be more compelling to others), while other parts seem to be going more for minimising-net-suffering / maximising-total-wellbeing kinds of metrics.

I'd suggest reading prior discussions of the so-called "poor meat eater problem."

I see a few problems with this argument. (These are mostly not original ideas.)

• This argument would likely reflect badly on EA and/or animal advocacy if it became more common and more public. Unpopular arguments may be worth it if the benefits of arguing them outweigh the costs, but that seems unlikely here.
   
• If you believe farmed animal welfare is the cause area that warrants the highest priority, then you should be looking for the most cost-effective interventions within that cause area. There are interventions in this area that seem very cost-effective, such as corporate campaigns, and it seems unlikely that persuading EAs working in global poverty that their interventions are harmful, or pursuing human population control interventions instead, is anywhere near as cost-effective.
   
• This analysis looks at one potential flow-through effect of EA global poverty interventions, and does not consider any others that could potentially benefit animals:
  
  • Good things can lead to more good things, e.g. Open Phil has recommended $80 million in effective grants towards farmed animal welfare, but they would not exist if GiveWell had not established their credibility in global poverty. (Open Phil started out as a GiveWell project called GiveWell Labs.)
  • Solving human problems may free up resources for solving animal welfare problems.
  • Increases in human population and/or consumption may lead to decreases in wild animal populations, which may reduce wild animal suffering.
     
• It's better if EAs working on global poverty and animal welfare are cooperative rather than antagonistic.

It's worth thinking about how significant the meat eater problem actually is for each intervention. In developing countries, especially those where GiveWell-recommended charities work, animal product consumption already tends to be low. Don't quote me on this, but I think animal farming is also less intensive in these regions. Of course, these countries are developing, and their animal product consumption is expected to increase, and we might expect farming to intensify, too. Furthermore, there are usually fewer legal animal protections or none at all, so slaughter might be particularly bad.

EDIT: kbog made some estimates. See this post. He concluded:

Increasing annual income for a poor person by $1,000/year has a farm animal welfare cost equivalent to adding several weeks of misery. To me, given the direct noneconomic benefits of efforts such as malaria prevention and deworming, such efforts seem robustly good enough to outweigh the animal costs in the short run. Things like industrialization and GiveDirectly seem to have unclear short run welfare impact, depending on the characteristics of the recipient populations

See this chart by Fauntalytics from this post or the FAOSTAT database, and check the different groups of species; chickens and fishes are usually the most consumed by numbers (although fishes are counted by weight, unfortunately); the countries where GiveWell-recommended charities work are towards the bottom right. Some countries are listed here in the first column. GiveDirectly's beneficiaries are on the lowest end in Kenya, Uganda and Rwanda, with around 0.5 chickens per capita per year. On the higher end (as far as I know, for the countries from that spreadsheet), it's around 2.8 in Senegal, 3 in Burkina Faso, 3.9 in Cameroon, and 5.6 in Togo. For reference, it's 28 in the US.

I also don't know how long chickens live in these countries before slaughter; fast-growing breeds are slaughtered at around 40-50 days old and have various welfare issues as a result of their accelerated growth, but these are basically the shortest lives for chickens (other than chicks slaughtered at birth in the egg industry), and I'd expect such breeds to be less common in regions where GiveWell-recommended charities work.

Furthermore, health interventions might reduce fertility, although GiveWell expects life-saving interventions to accelerate population growth.

• Improving health or wellbeing without increasing longevity, e.g. preventing blindness (increases consumption by freeing up money otherwise spent on healthcare or wellbeing)

This seems unlikely to be significant to me. In many cases, they just don't have access at all without outside intervention, so they won't be spending more on healthcare or wellbeing. That being said, better healthcare and wellbeing often leads to higher productivity, which could lead to increased consumption.

For anyone interested, there are some charities working on family planning (which reduces births) that are EA-recommended or EA-aligned:

1. Population Services International, recommended by the Life You Can Save, although they don't exclusively work on family planning. They are not GiveWell-recommended.
2. Development Media International, a GiveWell standout charity, also does some work on family planning, although I think it's only a small part of what they do.
3. Family Empowerment Media, just incubated by Charity Entrepreneurship. Charity Entrepreneurship also included externalities on animal welfare and climate change in their report, and it looks very cost-effective on both counts, although the charity has roughly no track record, since it was just started. EDIT: The report was modelled primarily based on Ghana, where the per capita chicken consumption is 3.2 per year, around the higher end where GiveWell-recommended charities work, so this might suggest the meat eater problem is actually significant for life-saving charities, since you'd expect similar externalities on farmed animals. It looks like they're starting in Nigeria, though, where per capita consumption is a bit less than 1 chicken per year. (Disclosure: I'm an animal welfare research intern at Charity Entrepreneurship.)

Personally, I think a hedging approach is reasonable. I wrote a post about hedging, but see this comment thread about the meat eater problem, specifically. I would say that those donating to global health and poverty who are really unsure about how to weight animal welfare relative to human welfare might also want to donate to animal welfare or family planning (unless they think nonhuman animals hardly matter at all compared to humans). Between global health and poverty, and animal welfare, I think those who think that farmed animals matter a decent amount compared to humans should mostly support animal welfare. See, e.g. this post comparing AMF and THL, although it doesn't include any meat eater effects of AMF and I'm personally skeptical of the (net) benefits of cage-free compared to caged for egg-laying hens, which has been a major focus of THL until recently.

I decided to add an EA Forum tag for the Meat-Eater Problem, and I tagged the posts discussing it that I could find through the search function. So you can see some prior discussions by clicking on that link.