Finding the right moral goal can be difficult for some groups, and I think it is interesting to think about for whom this would work. For example, for someone who is active in a local community, such as an animal shelther, it may be a big step to take to want to help as many animals as possible, because you may conclude that you need to work on factory farming, and no longer help your dogs and cats.
I also think that the right moral goal may be very abstract, and thus very far away for most people.
Seen as a strategy for people already involved in EA, it indeed doesn't seem too difficult, but something interesting to research for yourself.
The link to the analysis from Givewell actually says that condoms don't seem to decrease the risk of HIV and other STD's.
I realized this is too difficult and probably not impactful enough to be scalable.
What I do want to say, is that EA has already impacted my life by making me a more informed citizen. I know understand more of the big problems in the world, have become more rational and can thus more easily judge what I need to make of the information in the news for example. It may not look very impactful to spend a lot of time reading about EA-related topics, but EA is difficult, and if we also want to have the right message out in one-on-one conversations, we need people in the community to stay informed of all the great ideas and ways of thinking out there.
I'm not sure this is a good idea, but let's stay creative: (internet) consultation in new policy. In the Netherlands you can do this for a lot of new laws of the central government. For a lot it may not be worth the trouble, but in some laws we may be able to find large improvements. I have the general image that in government, making the right laws is very difficult, and if you have strong arguments why a certain thing must be changed, people will go with that. Companies seem to often lobby for laws in their favor, we can do that to make laws and policies more EA-aligned.