Have you considered a Health Savings Account (HSA)? If you are in good health and rarely see the doctor for more than annual check-ups, then it might be a good option for you. Basically, it is like a bank account that you make monthly deposits into (you can even invest the money you put into the account, so it grows while it sits there) instead of making large monthly payments to an insurance company. Then, you pay out of that account for any/all healthcare expenses, from Tylenol to doctor's visits. The money you put into the HSA is tax deductible, and it stays there as long as you need it. The account usually comes with it's own debit card for use at the doctor's office. The only requirement is that you carry a high-deductible health plan to cover you in the event that a major medical issue arises. (Generally, a high deductible health plan is very inexpensive per month, like $20 a month, and carries a deductible of $2,500 or so, which you could pay using your HSA in the event that you needed it.)
Hope you find something that works for you! Good luck!