I would recommend both dietary restriction with low cholesterol and low fat, high fiber, and adding 1-2 servings of fatty fish per week.
I would also recommend starting a statin, which can reduce your risk of heart attack and stroke in the long term. With your extremely high LDL level even with diet and strong family history, I would consider the diagnosis of familial hypercholesterolemia, which is a genetic condition of high LDL, found to be caused by defects in the LDL receptor. I would definitely have your first degree relative checked for high LDL as well, including your children as fatty plaques in patients with very high LDL levels can start even in the early teens.
It will be interesting to hear what the expert thinks about this as there has been much discussion over statin use of late. I have used statins for years with great results and no adverse affects, but everyone is different. Like you, I exercise daily and watch my diet but that still was not enough to get where I needed to be. If you are already doing all the things you can to prevent high cholesterol like exercising and eating right and still have such a high LDL, you may not be able to overcome the risk factors you do not control, your family history and genetics. I would certainly take a statin in your case, but as I said everyone is different.
Side effect rates are reported between 1% and 3% with the most common being muscle pain. The 4S Study done to test the effectiveness and safety of Simvastatin shows a side effect rate of 1 in 2221. There are risks of more sever side effects but they are very, very rare. They include muscle damage, loss of memory, neuropathy and liver damage.
I'm sure the doctor will have a more complete response.
Jon