The EA strategy of private donation would sell well to Republicans: both to minimize suffering due to poverty as well as mitigate poverty's destabilizing effects in regions critical to US interests. Some of the Republicans I've debated about poverty pointed to the role of the private citizen, churches, and NGOs to do that, not the government.
EA also lends itself to a Republican emphasis on national security, particularly nuclear strategy and short term artificial intelligence cyber warfare strategies.
The humanist/atheist, tech world, and Cali overrepresentation is probably the biggest reason EA is low on Republicans.
I agree that this has the potential to be highly impactful and it's definitely neglected. The fact that it can piggy-back on increasing exposure to non-EAs about EA topics makes this more persuasive, even if it the number of people helped might be small.
My only question would be whether that spare volunteer capacity could/would be used to persuade/train/target people within the DMV - since they are in a position to greatly increase the number of people who sign up by spending only an extra 2-3 seconds nudging people toward a yes, since it's a standard question for the driver's license application. I've read a study somewhere about how this was surprisingly effective - but I do realize this is a significant change in trajectory, but good to point out nonetheless.
I also see a potential upside of having more people wonder what other neglected topics can have outsized effects, thus a great lead-in to EA topics. If this were to become another cause area, it could garner some momentum, possibly enough to pressure some officials to contemplate an opt-out system, rather than the current opt-in system which would theoretically rid us of this shortage with only a nudge.