[einpoklum]

Well, as far as the time-consumption you could try Randomization:

Decide what fraction you want to give each of several projects (or make it uniform-probability), and partition the range [0,1] by those fractions. Now draw a random number between 0 and 1 (you can do this online if you like); give the $1000 to the project in whose range you've drawn.

I'm not saying that's such a great idea, but the expected donation to each project remains the same (well, depends on some ontological considerations I suppose).