Testing all the caissons would be unprecedented. If this were new construction with documented design and construction quality assurance, testing any caissons this large would be unusual. I would start by searching for the original geotechnical investigation report and the reports of construction inspection. Potential sources include the original building owner, the design firm, the geotech firm, the contractor or subcontractor, and the City building permits department. If you find those, you have as much as the original owner had available to rely on the caissons, plus a full-scale load test of every caisson! If you are not planning to exceed those previous loads, why would you want more? This assumes, of course, that there was no record or visible evidence of poor foundation performance.
Caissons on competent rock rarely fail by excessive settlement or bearing capacity failure. The failures that have occurred were usually due to some construction deficiency, such as entry of water or soil into the concrete during placement. The PIT test should be able to verify the competence of the shafts down to the top of the bell. That would not be expensive. A few cores through the bell and into the rock should give a general check on the quality of construction, including the concrete quality and the cleanliness of the bearing surface. Generally, that was better 30 or 50 years ago than today, because down-hole cleaning and inspection were common practice.
Find a well-established local geotechnical engineer and get his advice and perspective.