I think wanting to help is great and I don't want to discourage you from exploring different ways to do that or poo on your parade...
but as a shelter person, because of all the tragedies and sketchy people out there, I would only be able to send dogs to a reputable rescue who would then take responsibility for that animal and I think that's going to be the case most places you look. It should be anyway.
And sadly, brokering long distance adoptions seems like it would help but you end up with so many disasters, even when the people are great and everything's on the up and up, it just doesn't work out - and what happens to the dog then? They're hundreds of miles from where they started out.
Also, keep in mind that most shelters have little info on the dogs and even if they are able to do a good evaluation (rare) the personalities of dogs in shelters are often wildly different from their "true" personalities. I foster all my dogs at least a couple weeks before I even think about placing them because it takes that long to know what sort of dog you've got and where they'll be compatible. Sending dogs straight from the shelter into a home, you will get a lot of dogs that bounce back and there needs to be a safety net. If you're assisting with placement, there are also liability issues to be concerned about. What if the dog you gave them bites someone?
My suggestion would be to some sleuthing around and see if you can find a group in your area to work with which will give not only the dogs but YOU a safety net.
Sorry to come off as such a downer because I really do want to commend you for wanting to help and getting on here to ask good questions! Anything's doable, just very very important to walk into it with your eyes wide open.