What can be done to reverse the clogging of your arteries after a lifetime of eating things that would clog?

Many factors. Evaluation by a primary care & cardiologist, reduce weight - BMI < 28, eat right: low fat, low (bad) cholesterol, consider high quality fish oil, cessation of smoking, exercise (if you are healthy enough per your physician), reduce alcohol consumption, take prescribed medications as directed. Know your numbers: cholesterol, blood pressure, blood sugar and work with your physician to optimize them.
Statin. A combination of maintaining normal weight, regular exercise, avoiding tobacco, vegetarian or mediterranean diet, control of bp, and use of a statin and Aspirin would greatly lower risk, even after a lifetime of inattention to risk.