A donor lottery could come with an agreement (which can only be enforced by honor) to actually spend at least 100 hours considering the decision. We may also want there to be a norm against the decider explaining their reasoning, so that the 100 hours get spent on trying to optimize the decision rather than defend it.
If I won such a lottery, I'd in fact spend my first hour coming up with as many candidates as possible for better targets than my current favorite, do some winnowing and triage, and try to actually look for cruxes between the resulting choices.