There's a well in Alaska that I believe is producing and it's at about 21,000 feet. Whether a well is economically viable depends on the material it's drilling through, as well as the depth.
You asked about the deepest organic material; the deepest discovery you linked ("The well, located in Keathley Canyon block 102, approximately 250 miles (400 kilometres) south east of Houston, is in 4,132 feet (1,259 metres) of water. The Tiber well was drilled to a total depth of approximately 35,055 feet (10,685 metres) making it one of the deepest wells ever drilled by the oil and gas industry. The well found oil in multiple Lower Tertiary reservoirs.") to was from the Lower Tertiary, which began after the K/T Extinction Event. There are plenty of fossils from very much older periods of time.