I suggest that you keep the bill from the provider, in addition to the EOB. I also suggest that you keep the complete credit card statement, not just the details of individual transactions.
Basically what you are doing seems reasonable. It would probably be sufficient if you were audited now. But 30 or 40 years from now, who knows what the rules will be? No one can tell you with certainty what the IRS will accept today, much less 30 or 40 years from now. So you are taking a slight risk that an examiner in the distant future will not be satisfied with your records. I wouldn't worry too much about it, though. It will probably be fine. But that's just my opinion. It's also quite possible that the IRS will not question what you report after you retire, so don't make yourself crazy about it.
You also need to think about how you are going to preserve your records for 30 or 40 years. Archival storage is not as simple as packing it away and forgetting it. It's an active process. If you are keeping paper records you need to have backup in case the paper records are damaged, lost, or destroyed. You could keep duplicate copies somewhere else, or keep electronic copies of the paper records. You also have to keep the records well organized, protected from deterioration, and keep track of where they are if you move, so you can find them if you need them.
If you are keeping electronic records, either primary or backup, you have to stay in touch with changes in technology. Thirty or 40 years from now there might not be any software or device that can read a file that you save today. You might have to convert files to new formats and new media from time to time. Also, magnetic recordings and solid-state storage do not last forever. You probably have to make fresh copies from time to time to make sure they are still readable.
As far as a payment plan is concerned, Bsch4477 is correct that it won't matter. The basic concern with a payment plan is when the provider actually gets paid. If you make payments directly to the provider, then each payment is counted as a medical expense on the date that you make it. You would need records of the individual payments. But if the payment plan is a loan from a third party, you paid the medical expense when you used the loan to pay the provider. Your subsequent payments to the lender are not medical expenses. This makes a difference if you are deducting medical expenses in the year that you pay them. But 30 years later the distinction won't matter.
