Posting here on the forums seems like a good start— you may get some interest just by asking the question.

As for other places to look, you could try posting on the EA Work Club or the Effective Altruism Job Postings Facebook group. Those seem to be dominated by listings for bigger/flashier roles, but I suspect many people would like to work on smaller projects.

Depending on what level of experience/qualification you're looking for, you could also try getting in touch with local EA groups that run out of universities. There may be students who are familiar with the subject area, have access to paid journal databases etc. and would be interested in part-time work on an EA-related topic.

I somewhat fit into that category myself. I'm a student, work on contract as a research assistant for my university, and would be interested in picking up further hours on an EA-related literature review/research project.

I probably wouldn't be the best choice in this case, as I don't have a background in animal welfare. But I imagine there are other students in similar circumstances who might have the right background knowledge to be a good fit

I'm definitely in favour of this kind of project since I feel more EAs should be experimenting with small projects.

Seconding Rowan_Stanley about just asking on the forum about specific issues, or in the Effective Animal Advocacy, Veggie EA Hangout or Ethics and Animals (not specifically EA) Facebook groups. You can also reach out specifically to (people who do work for) Animal Charity Evaluators, Sentience Institute, Charity Entrepreneurship, Rethink Priorities, or the Animal Welfare EA fund.

I think you might as well see what you can get for free. It's also useful for others to see the discussion if you post it on the forum or in a FB group, and people interested in these topics are often interested in discussing them, too, so I would not see it as imposing on others to just ask.

I also second Rowan_Stanley's recommendations for places to look for research assistants. I'd be interested myself, but I don't think I can commit now.