OP here....
Well, my 86-year-old father-in-law came over to supervise my work. Before I started, he insisted that I dig 12 feet from the start of the line about where my snake would come to a complete halt.
Did not want to...but in interests of marital harmony....found the drain line runs alongside the house and ties into another drain line that is about 20 feet away....and the line is all tile drain.
Four sections (four feet) of said tile drain were nearly completed stuffed with fine dirt from the overlying rose bed. The rest of the line to the tee with the other line was clear.
Under father-in-law's direction, removed the tile from the start to about 20 feet in, where the tiles were all clear.
Using flexible clay to sewer coupling, hooked up solid PVC sewer pipe (3000-pound crush), stuffed a hose down the downspout and let the water flow. No leaks, good flow.
Backfilled, we have had a few days of good heavy rain and no problems.
Lessons learned....And thanks for all the suggestions.