Usually when people buy shares they are going to try and get the most shares for the least amount of money, but the incentives are a bit different for stock buybacks. I don't know if buybacks are large enough to "move the market" but I'd be curious to see details on how exactly orders are placed.

I'm a big believer that we need more non-profits that simple exist to employ people and provide goods and services. I realize this is just a charity and depends on the good will of people with capital.