Experiment #1: Effects of meat on Bilirubin levels

Standard blood work has always shown a high bilirubin level for me for as long as I can remember.  Doctors generally shrug it off as "gilbert's syndrome" and don't think much of it.  They say 1% of the population has abnormally high levels and it doesn't mean anything.  I'm not so sure that is correct any longer.  My bilirubin level is typically in the low 2's although more recently it has come close to 3.0 but goes up and down from test to test.  I've been dealing with a lot of fatigue issues more recently following a Celiac diagnosis.  Aside from the bilirubin level out of whack, everything else is normal.
About a month ago I had accidentally avoided red meat for a week just before a blood test, eating chicken & turkey products as my meat.  To my shock, the bilirubin level measured came out to 1.3, still slightly high but much lower than it had ever been.  This leads me to the theory that red meat might be responsible...  it could also be the fat content of the meat rather than the "red" variety.  Sunlight exposure is another possible variable here since I have read that sunlight helps the body break down bilirubin.