A nonprofit that spends 1% of its funding on fundraising and barely scrapes by each year will be rated as more cost-effective than a nonprofit that spends 10% of its funding on fundraising and grows its donations by 15% a year, even though the latter is ultimately going to be able to devote far more resources to its programs.
But maybe they can't organize around your cause because the coordination and scale is too large. That's what large non-profits are good for. They burn efficiency on overhead, but can coordinate larger and grander projects.
It's a whole ecosystem. Experienced people are almost never comparing the cost-efficiency of a small organization and a large one for the same cause; they're using it to compare peers within whatever other criteria.
Raise a bunch of money, get an endowment going, and regularly fund medium size/medium usefulness projects both in a continuous way and on a grant-for-feature/limited-project way. Trying to focus on quality so most of the money goes towards people who actually get things done (as opposed to funding awareness, funding fundraising, and misc “not doing things” efforts) not that none of that overhead stuff would get done, but only a quite small portion.