Will Gut Thrive eliminate my need for a prescribed daily dose of mesalamine and azathioprine for ulcerative colitis (with the occasional need for a short prednisone regiment to tamp down flares)? If so, when can I stop taking them?

Continue your meds as normal, and as your body responds to the program and you get healthier, you should be able to go back to your doctor and have him lower your dose incrementally until you ideally don't need the meds anymore. He/she will have to guide you responsibly based upon your individuality and how your body responds to new healing directives.