Wisconsin State Rail Map
Too bad there isn't a good way to have the train enter Madison from the southeast (through McFarland), then up the isthmus to a stop at Monona Terrace, then up to a stop at the Madison Airport, then continue on to the north and west. Then there would be no back-up movements.
One option is to take the WSOR through Waukesha, Whitewater and then up through McFarland. It would miss the important areas in Lake Country and a mid-sized city at Watertown, but you'd hit downtown Waukesha, and could have a nice west suburban park-n-ride stop near the West Allis / New Berlin border. Would also get very close to the Janesville and Beloit markets.
Another option is to build a new 19 mile rail line from Waterloo southwest to McFarland. There is open country there. This is a much less likely option but would keep the train from seemingly swinging far south.
Regarding the Madison airport: That should be either THE Madison station or the north suburban stop. The infrastructure is all there already. Parking for suburbanites or people coming from around the region. Car rentals for people coming into Madison that need a car. A nice opportunity for multimodal transportation with airlines. And the train line to Minneapolis goes right by it. I think it is a no brainer to have a stop there.
However, I do feel there is a large market for people wanting to come to Madison, get off the train near downtown and/or campus, and walk where they need to go. A stop at the airport or even the near east side just wouldn't maximize the draw to the train for those customers. If Madison was the end of the line for the train, then a downtown station would be fine. But with the back-up move needed and the time it requires, it would significantly hurt the through passengers and those numbers.
Perhaps a near east side stop could have a streetcar or LRT connection to downtown and that would draw in more of those walking customers, but it would still add a hurdle and hurt their numbers. You could have a bus shuttle too; but personally I'm not riding the train so I can take a bus to my destination.
It could be possible that the four trains a day that are through trains utilize the Madison airport station and not downtown. And the six trains a day that terminate in Madison, use the downtown station and don't use the airport station. My worry with that solution is that too many customers will go to the wrong station.
I don't have the answer for Madison. It is a complex problem with competing interests from through passengers and the significant downtown / campus customers. That's why I'd love to see a solution like I proposed at the beginning, to have trains enter via McFarland. I think that would solve a lot of the extra time issue, and allow use for both stations for all trains going to/through Madison.