Thanks for these responses. The sample-and-scale approach occurred to me. I think a simulation would give me a sense of how badly it would violate my ranges.
@Camillio: I was unaware of the Dirichlet distribution. It looks like the right answer, though if I use the simpler, direct approach...
I teach cost-benefit analysis, which requires me to teach monte carlo simulation for sensitivity analysis. I use excel. I understand how to generate a number with uniform, triangular, normal or other distributions, but I don't know how to randomly generate a set of numbers between zero and one...