Problem somewhat solved. Since I was unable to find anything to take other than a door, I took a door. They scanned it to get the color. The salesperson then mixed the paint with a little less coloration than the color scanner suggested. When we painted some on the door, it didn't totally disappear, but it was close enough. (The scanned formula was probably the right one, and I didn't want to wait longer to do trial and error for a single gallon of paint.)
What was neat is that I had the labels from about five cans of paint that had been used at the house previously. The salesperson got the job numbers off of each can and was able to pull of the orders. There was a can of white on one of the orders for which I didn't have the can. Our guess is that it was the missing white paint. It threw us a little bit of a curve because it had some gold and black in the formula. In retrospect, I should have gotten that formula as I now believe it to be the exact one.
After all that, it turns out that it didn't really matter. When I started prepping the door, I saw a few spots where the paint was flaking off. After using a paint scraper and sandpaper for an hour, most of the original paint was removed. It had not adhered well to the pre-primed door. If the original paint did not come off with the beating I gave it, I assumed it was sufficiently adhered to paint covering it, so I painted over it.
I painted the door in the driveway, and I wasn't done until the temperature started dropping. A couple of hours later, the paint was still wet in a number of places. I brought it inside the house and stood it up to dry. When I checked it this morning, it has fully dried. It looks great. It doesn't look like it needs a second coat, so I'm not sure if I will add one. The slow drying time may have allowed the paint to level more than it normally would. The brush strokes in the inside of the panels are not really obvious.
Being a perfectionist, I'll probably paint the other side. That remains to be seen. The other side looks fine, but I'll have to examine it in better light. The side I worked over was in much worse shape than I thought it would be.
My next dilemma is that the paint is peeling off of the molding in several places in the house. That says to me that the wood was not properly primed to allow the paint to adhere properly. If that turns out the be the case, I could have a major operation on my hands. One thing is clear. Whoever owns this house next will be able to say, "The previous owners took really good care of this property."