That article brings back fond memories for us.
In 2009 we did an Oregon Trail trip and loved it. We started at the National Frontier Trails Museum in Independence, Missouri and then followed the book "The Oregon Trail Revisited" by Gregory Franzwa. After an overview and advice to travelers, it has chapters like "Finding the Trail in Missouri", "Finding the Trail in Kansas", and so on through Nebraska, Wyoming, Idaho, and Oregon.
We visited river landings, wagon-track swales, the points of interest in the Smithsonian article, national museums, county museums, town museums, campsites, river fords, frontier forts, etc. We drove many miles of back roads and walked miles of cow-pie-dotted prairie.
The book says it will take three to four weeks and for us it was just under four. The last chapter ("The Speed Trip") also describes a ten-day route.