Your leukocyte count is normal, so don't worry. I don't know anything about mobile cecum syndrome other than it has been seen as a potential cause for IBS. Management of constipation predominant IBS is difficult, but the best way to start is talking with your doctor. I know that's not really what you want to hear, but if your doctor is using Rome Criteria then he/she is obviously educated in the realm of these disorders. Most people get the diagnosis after months and months of tests that show nothing.
What I can recommend trying, without having any medical background - is to look up the FODMAP diet. It helps with bloating and gas.
I hope you get some good help.