I would recommend cloning your protein into a TET-inducible vector or a vector with a weaker promoter such as EF-1 alpha. You could then perform clonal selection on a heterogeneous population of cells expressing this construct to identify a clone that expresses lower levels of your fusion protein which do not alter the phenotype of your cells. If you image your cells in a low background medium like FluoroBrite DMEM, you could try reducing the intensity of the light source to minimize any cell damage resulting from excessive excitation of your fusion protein. If neither of these options work, consider validating the findings of your imaging experiments with an alternative non-image-based cell or biochemical assay that doesn’t require exposure to fluorescent light or the expression of a transgene.