I have no idea about blood tests that might be a good indicator for performance of broilers, as it is not my field of expertise.
Measuring stress might be quite complicated, as it might be quite difficult to distinguish between the stress induced by catching the animal and taking the blood sample and other possible causes.
I remember that my late colleague Gerard Beuving, took a lot of precautions and used tricks to be sure, that when he took the blood samples of laying hens to measure corticosteroids as an indicator of stress, that the hens were not aware of his presence or him taking the blood sample.