The most cost-effective way to do this is to find someone else who's already doing it and draft in their wake. Volunteer, donate money, get on their board, etc. Your money will go so much farther if you can avoid all the admin costs.
this is exactly what I do not want to do, although I appreciate that perspective. I agree - giving money is the easy way. And while I admire many dedicated shelters and shelter staff - that is not where I want any strays to end up if I can stop it. It's great if they are adopted in a month or so, but when I hear these stories of animals being in shelters for years - my heart just breaks. I'm not looking to maximize my efforts in any grand scheme - I'm looking for a way to be able to directly help the animals I see out my front door and maybe help just a few others here and there to do the same.
I think you might be underestimating the amount of admin time and expense involved. It doesn't sound like you're interested in all that, nor do you need to be. Here's an example I'm familiar with:
https://arflife.org/ BTW, they only take animals from shelters and they are a no-kill operation. The LaRussa family is no longer involved [dramadramadrama], but the good work continues.
Getting involved with a larger operation means more animals will be helped.
As to those "articles" about animals kept in shelters for years, many of them are just tugging at your heartstrings so you'll open your wallet. Not criticizing you, just suggesting that emotions sell.
Anyway, good luck reaching your goal, whatever form it takes.