Implications of Atrial Fibrillation and anticoagulants

First, hi to all.  I have gleaned invaluable information from these forums, keep up the good work.
My question relates to Atrial Fibrillation in conjunction with Hypertrophic Cardiomyopathy with first degree AV Block and Left Bundle Branch Block. I have partial obstruction of opening of Mitral Valve and moderate Subaortic Stenosis.
I am a 57 year old Caucasian woman and I have fairly frequent Angina and Palpitations which have been previously connected to PVC's and Ventricular Tachycardia. My A-Fib is intermittent and occurs a couple of times on 24 hour Holter Monitor.
My Cardiologist insists I should take anticoagulants.  I am on a high dose of Levothyroxine due to a history of two different types (Papillary and Follicular Variant) of Thyroid Cancer tumors. I also have severe Sjogren's Syndrome and Fibromyalgia with joint inflammation for which I require 2400 mg of Ibuprofen per day.  I have had a small bowel resection for obstruction from fibrosis and I have moderate diverticulitis with intermittent bleeding.
1.  Since I cannot take aspirin with Ibuprofen, is Warfarin my only option?  
2.  If I decide to stop the Ibuprofen, is there another Anti-inflammatory I could take that would not be contraindicated with Aspirin?
3.  Can I just ignore the A-Fib, i.e., is the Ibuprofen supplying sufficient Anticoagulant effect to prevent Stroke?
Thanks in advance for your answers and advice.  I will be speaking again with my Physician very soon, but I would like to get some other opinions so that I am, at least a little. informed on my possible options.
Thanks to all and this is a wonderful forum.
Stephanie