I actually travelled to Singapore and Bali last March so I feel your anxiety about
the trip. I also had many stopovers, in Detroit, Narita then Singapore for a few nights before we left for Bali. On the way home we did not overnight in Singapore so I can honestly say I didn't sleep too much. I was flaring at the time of my trip too. I just always make sure to have plenty of extra medications with me, even if I'm not taking them at the moment. Especially TUMS, GasX, hycosamine (some people take Bentyl) - I even brought my Metamucil with me and a little plastic spoon just to make sure I could always take it! I always find just making sure you can stick to your normal routine, even with such a drastic time change, can help. Trying to get as much sleep as possible helps too.
I just got back from a week in Spain and although that wasn't as long of a flight or as much of a time change, I still made sure to have all the extra meds with me. I even took extra prednisone just in case I for some reason started getting sick and needed to up my dose. Better safe than in pain and sick during a vacation, that is how I think of it :)
Have a good trip!