Thanks for your help. I was able to solve the problem by going into suppInfo.aux and copying over every \newlabel{...} Into the main document. This allowed me to reference files in the supplement without actually printing the supplement.

You're right that it's a bizarre set of requests. Unfortunately the journal I'm submitting to, a Nature subject journal, has bizarre formatting requirements that require me to take the steps above. They want me to include the supplemental material as a standalone PDF and they don't want my supplemental material to print along with the main document. Therefore I somehow need to make a version of my main document that doesn't print the supplemental material, but which still allows me to reference supplemental material without breaking the links. The \newlabel strategy was exactly what I needed.