After much banging my head against the desk, I'm fairly certain I figured this out. There was one variable that was contributing to the derived quantity that had a variance that was much larger than the other variables- when fitting the model, I would get the warning:
lavaan WARNING: some observed variances are (at least) a factor 1000 times larger than others
I had read in other threads on here that this warning "usually" didn't cause any problems. However, after dividing by the variable by 10 to reduce its variance, the unstandardzied and standardized estimates make more sense and have the same sign, so perhaps my model was an example where the warning did matter.
I can still to upload an example if it would be of interest.