I am an artist who would like to email a few photographers requesting permission to use their photographs. After viewing their online portfolios, I was hoping that they had some specific images not posted that I could use and re-create in my drawings and paintings that involve the same subject matter. Most of the photographers work across seas traveling to places I can not travel to. It would be sold (hopefully) and of course I would also pay myself. However, a good majority of the funds acquired would go to a specified humanitarian non profit organization. I have no idea on what to really say in order to pursuade the photographer(s) that I am I have no intentions on taking credit for the photograph, just re-creating it in a different art form & shedding light on the subject.
Just tell the truth, whole of it. If they are amateur*, they should be pretty open. If they are doing it as their profession, they will actually want to sell rights. Nothing wrong or difficult either way - you just mail, describe what would you want to obtain and they will name their price and conditions.
If you are not willing to pay them at all, but you are willing to keep some money to yourself, it would be unfair. Your artistic tools and materials aren't free, all right, but camera isn't free either, nor is travel. The only realistic chance to obtain rights for free if you are donating all to charity. If you are donating everything above your costs, it's only fair if you are prepared to offer photographers to cover their costs - then you can ask them to "donate" rest to charity, too. But don't be disappointed if they refuse, and don't try to play morality tricks on them. They and their kids got to eat, too.
Last but not least, you will be asked to show photographer's name on / with your work. For commercial ones, marketing value is the least thing they can get from charity auction if you are only covering their costs. For hobbyists, well, if they keep good portfolios online, it proves they do want appreciation.
Important part, as pointed in comments, is what kinds of rights will you obtain. There are exclusive and non-exclusive rights, meaning that either you will be the only one with permission and license to use said photo, or that you will be allowed, but others may get licensed just as well. I wouldn't expect exclusive license for anything less than usual commercial price. With non-exclusive permission, author is still able to earn on his photo - prior permission for one painting will be only a slight hindrance.
When asking for license, don't forget to make clear what control you will have after image is sold (basically: none) and that it might be customary (depending on country, I guess) or explicitly stated that painting's author is not paid for exhibitions, prints in gallery or museum guidebooks and so on. You know that better than I do, I'm sure. And probably better than photographer you will contact. Failure to state how obtained permission will be used might result in legal problems for you, and, in the end, you might end up paying much much more than full exclusive unlimited commercial usage license would cost you.
* Amateur as in "not doing it for money", not as in "bad".
Strictly amateur viewpoint, so I'm covering the social aspects, not the legal ones:
What you said in your question sounds pretty good! If you have an online portfolio of your own work it might be helpful, humans like to do a bit of research into these things.
I have in fact had people ask to paint my photos before, and they simply said "I love your photos, could I paint them, this is what I intend using them for."
I personally said yes on principle because I have great respect for fine artists (not least because I married one) but the not-for-profit element would seal the deal for me anyway.
I would specify the actual organisation you are donating to; if you are worried that a specific organistion might put people off if it is not a cause they share, well, it's a risk, but I would be more wary that a vague "oh, it'll go to some charity or other" doesn't sound convincingly like it would be honoured, and would put a lot more people off.
I loved seeing the end result, too. I personally would not consider a painting to be in any moral way (as I said, I am ignoring all legal points) a duplicate. The artist will always add their own interpretation.