Would you pursue more dedicated stone surveillance imaging testing for a patient with recurrent nephrolithiasis who has PET-CT scans twice yearly?  

Unless the patient is symptomatic, I am not sure there is a reason to. Though PET CT is not the best imaging to look for stones.

Serial CT scanning is my preferred imaging modality for assessing stone volume and, hence, metabolic activity. I have not personally used a combined PET-CT. Assuming the images are still satisfactory for detecting small changes in the stone volume, I think it would be an entirely satisfactory kidney...

If all of the CT exams are after contrast, they cannot be used for stone counting. I would ask for pre-contrast images on the CT.