There are a number of qualified inspection companies that have experience with coke drums. A company called CIA Inspection has the ability to perform internal visual inspection using high definition cameras, laser scan to determine the shape of the coke drum and to monitor any bulges and to do robotic crack inspection using a technique called ACFM (alternating current field measurement). Other companies, Mistras and IRISNDT, can do video and laser scanning.
All of these companies can employ a wide range of inspection techniques, such as phased array UT, TOFD (time of flight diffraction), ACFM, acoustic emission and others. As you indicate, the change in materials can be a challenge for some of these inspection techniques. You should have discussions with an inspection company that has experience with inspecting coke drums to determine the proper techniques to gain understanding of the condition of the drums.