< the first 2 stages are going very close to a road >
For the first stage, it is true, in part. The entire Giswil - Flüeli-Ranft stage is on tarred paths. From Giswil to Sachseln, however, it is a pedestrian path, along the scenic Sarnen Lake. Then you go through the village of Sachseln, and go up to Flüeli on a low-traffic road. Not the Switzerland Alps you are dreaming of, but maybe a good way to give all of you some training on hiking. This stage is Stage 17 of the Trans Swiss Trail.
The second stage is away from any road, except the section I recommend you do by bus, if you spend the night at Flüeli. You have to walk across the valley to St Niklausen OW from where you catch a postal bus to Melchtal or even further into the valley. Then you take the Obwaldner Höhenweg Trail to Eggen. When we did this, we took steep trails from Melchtal to the said trail, but there are alternatives, that will avoid some or all the steep parts, if you go to Stöckalp, the end station of the bus, from where you can start hiking, or take the cable car further up to Melchsee at the beginning of the Obwaldner Höhenweg Trail. At the other end of the trail, at Eggen, you can take a private cable car to bring you to the bottom of the Engelberg Valley. You won't be able to boast to your friends about the Matterhorn, but instead you will fascinate them by telling them how private cable cars operate. When you arrive at Eggen, you must use a telephone that is there, and order your private cable car ride. You pay the ride at the middle station, and go down to Mettlen, from where you walk on a path (not the main road) to Grafenort where you can take a train to Engelberg.
Now, you need to know about postal buses and trains. Check out HOW TO TRAVEL on top of your screen and navigate from there.
By now I hope you did not try to follow my description on Google Maps, if you did you must be frustrated indeed.
< Is there a more detailed map available online for such route planning? >
Yes, it's called Switzerland Mobility, check the boxes "Hiking", "Rail/bus/boat", and maybe "Route numbers". The base map is the Swiss Topo Map, and trails are highlighted in green. These trails are blazed with yellow signs. Train stations and bus stops are shown. If you click on a trail, you may get additional information. This is free. For CHF 50 per year, you can access Switzerland Mobility Plus which allows you to design your own itineraries and download the tracks as *.gpx files on your GPS.
Let me see if I have some photos of these hikes. That would be in a next post.