Niacin is often prescribed to help raise HDL. Exercise is beneficial. Still, most people see only a modest benefit for all their efforts. Have you ever heard of Dr. Esselstyn? He is a former Cleveland Clinic doctor, now retired, who has found that a plant-based diet can halt or even reverse coronary heart disease. It's worth looking into, in my opinion. Also, your dad should consider a completely trans fat-free diet - absolutely nothing partially hydrogenated.
Stress and Diabetes are two other huge risk factors that can cause blockages by causing changes in the heart arteries, and exercise is of course essential to healthy arteries. Also, once the arteries have particulate built up, they can clog up faster. Of course, one can't smoke with cardiac artery disease.
It isn't just about HDL levels. It has become apparent that there is more than one type of LDL. There's a dense heavy tiny LDL, and a larger light LDL. The small dense ones are the ones which get into the artery lining and cause the disease. Looking at diets with high levels of heart disease around the world, the common factor doesn't appear to be fat. It appears to be processed sugars. Soda drinks etc are packed with it, so are ready made meals etc.
There was the idea that high triglycerides is a flag to suggest an abundance of the high density LDL, but your Fathers trigs seem very low. And on the other hand his disease is increasing, suggesting that there is an abundance. HDL doesn't seem to affect these special high density LDL. They are produced in the Liver when lots of sugar or alcohol is consumed.
I don't know of any foods which particularly raise HDL, I just know that good exercise can raise it. When exercising, you release fats to use as energy so its ready for when the carbs run low. Your body creates lots of HDL to keep the LDL in balance during that time. I've seen this many times in people where they reduce the LDL, and the HDL reduces too. I think it's because the HDL production is triggered by the LDL production or amount in the blood.