Running FindVariableGenes() and RunPCA() again on the integrated dataset does not seem helpful to me because the limited feature space of 3000 is not changed. The alternative would be to subset() the population of interest and run the complete preprocessing including integration only on those cells again. That enables to change the feature space.
How to re identify variable genes on integrated data?
We do not support the identification of variable features on integrated data. If you want to subset and recluster using a new set of variable genes, you need to switch the assay of the subsetted to the 'RNA' assay. [source]