I am a longtime cardiac nurse in a major cardiac center. The reason I said you should consider paying out of pocket to see the best cardiologist you can find is because we regularly see people who do this. They come from all over the country (and even the world) after going online and referring themselves when they've gotten tired of all the run around and realize they need to get help despite obstacles in front of them. We are often amazed at what we see.
As I see it, if you've in fact had two heart attacks, not only should you be seeing a cardiologist regularly, you also should have been enrolled in a cardiac rehab program. It is vitally important that the cause for these heart attacks is found and steps taken to prevent further attacks. You have a long life to live ahead of you. That's problem #1.
Problem #2 is that a resting heart rate of 120 is too high, particularly after a heart attack (i.e. damaged heart muscle X2 in your case) and here's why: when your heart beats that fast, the chambers in the heart cannot fill all the way. Your heart has to beat faster to get the lesser amount of blood out in order to meet the demand of your organs. It becomes a viscious cycle. This unnecessary strain over time can cause your heart to enlarge to accomodate this extra demand. If it goes on for too long, cardiomyopathy and/or heart failure can result, this is why it is vital to get help now. Chances are you would be started on something like a beta blocker to slow your heart rate and promote better filling, thereby lessening the strain on the heart, and perhaps helping all the other systems in your body when they are better perfused. (Studies have also shown that after an MI beta blockers, ace inhibitors and statins can preserve cardiac function and improve survival so I am surprised you are not on any of these).
An ECG will show lots of things: previous MI (heart attack), heart rate and rythm (whether it is an abnormal rythm or just a tachycardia), strain, conduction disturbances, and a host of other things. It is a very inexpensive test. Based on that and a physical exam a cardiologist will know how to proceed with you. It may cost $500 to see the doc and another $80 for an ECG (figures are just estimates and I could be wrong) but whatever it costs, it would be a small price to pay for getting your health and "preservation of cardiac function" in check, and they will help you "get into the system" from there (even in your own HMO), they may even have care coordinators to help you. Best of luck.