If you have graphic design experience, check out the on-going logo design competition at 99designs for the Singularity Institute. There are still 6 days left to enter and be eligible to win the $295 prize if your design is selected. Tell your friends with graphic design experience too. There are very few submissions currently.
Note: This is a blind contest. Designers can only see their own entries. All designs will be revealed when the contest ends.
If you're interested at getting a peek at the designs, they will be online after the competition is over. This is standard practice in 99designs contests to prevent designers from contaminating each other and having all the designs drift in a certain direction.
I think your points are good ones. I would note though, that:
isn't necessarily true when the thing they are donating is their professional work. The reason it's better to hire a good professional is that the professional is going to understand things about design and communication better than the person trying to get the logo designed, including things like how to craft an overarching brand that sends a unified message rather than a single cool looking logo.
I realize it's hard to tell how good a professional is though, and I don't have any advice on that.