In the interim, I stumbled across this HBR post by Michael J. Mauboussin, where he presents a four-step process for determining what to measure in an environment where the links between cause and effect are not always clear. Some people in his comments section take exception to one of his fundamental assumptions, but there are some things I like about his four steps, especially the second one:
Step 2: Develop a theory of cause and effect to assess presumed drivers of the objective.
This is the best advice in the entire post, and reminiscent of a point made by one of my commenters. The words here are chosen very specifically. Develop a theory of cause and effect to assess presumed drivers of the objective. The point being that you're not going to know coming out of the gate what should be measured--but that you have to start measuring something.
You shouldn't do it blindly. You need to think carefully, and make a logical argument for what should be measured and why. Then measure it and perform the necessary analysis to determine if it is truly linked to an actual driver of performance. If not, develop another theory and pursue that. If nothing else, the discipline required to execute such a strategy would be a valuable addition to your organization's performance.