If I have a genetic cholesterol problem, is there a safe way to wean and stay off statins? Is it possible with diligence to diet?

No clear answer. Generally, aerobic exercise & a diet low in saturated fat/cholesterol is good for keeping cholesterol controlled. Almonds, walnuts, tofu, fiber, plant sterols/stannols, fish oil, vegan diet can be helpful. In certain cases, some treatments are more appropriate than others; e.g. Fish oil lowers tg but can raise ldl; best off asking your family doc or getting 2nd opinion (genetic problems differ).
High cholesterol. Diet that is vegetable based can lower total cholesterol about 25%