The lake boat schedule on the Thunersee ( Lake Thun) changes from the limited Spring Schedule to the Summer schedule on May 13th:
www.fahrplanfelder.ch/ fileadmin/fap_pdf_fiel ds/2017/3310.pdf
On and after May 13th, there are a few runs with a steam powered boat (das Dampfshiff)
To learn more about travel possibilities between cities, you can use the timetable:
Please read the instruction page at that link.
The timetable covers all means of public transport...trains, boats, ships, and the pages linked above are copied from the printed timetable book.
To more easily understand the boat schedule on Lake Lucerne, you can also use:
Look under seasonal time tables. Note the change in schedules on May 25th.
There a link to a simplified map near the bottom of the page. The dots represent ship landings. There are several routes for the lake boats. Not all landings are reached on every trip. There are more routes available in the Summer schedule, on and after May 25th.
A useful map for planning travel by public transport is:
map.search.ch/?pos=680700,206724&z=64 &poi=haltestelle,mobil ity,zug
If you zoom in far enough, as I have done, you can see the train lines. In the menus, under "Points of Interest, Transport" you can turn on icons for the transport stops. It does not seem to show ship landings. But, you can zoom out to get an idea of the distances and train routes between cities. Turn of the transport stops if you wish. As you zoom out, there are too many blue dots on the map otherwise.
In theory, you can do all of the things you list, but that requires an elastic definition of the word "cover." You could cut back in the Bernese Oberland and spend some time at Luzern. (Note that he region is German-speaking, so that is the spelling you will see on signs. Also, in German, Lake Lucerne is called "der Vierwaldstättersee" which means "the lake of the four forest cantons.") Also, if you reduce your days in the Jungfrau region, you run the risk of not having a clear day, free of clouds ( at least at high altitude) to go up to the Jungfrau.
Most first time travelers find that the combination of Luzern and the Jungfrau region gives them more options for bad weather and to see/do different kinds of things.
You can check this link:
You would do a lot of traveling, and, in most cases, spend little time at each location. In one sense, the timing of your trip helps....many tourist activities in the Jungfrau region only become available on May 25th. For your specific interests, public transport or excursion cograil trains to Kleine Scheidegg and Jungfraujoch are available all year long. Their may be a seasonal gap in the schedules for Schilthorn (I don't remember when that is;check the timetable on your preferred dates) , but Mürren is always accessible by at least one of the two routes from Lauterbrunnen.
This map may be useful to give an overview of the region:
www.swissholidayco.com /Public/Assets/User/fi les/Map-of-Jungfrauregion1.jpg
I don't know about schedules at Zermatt; the timetable can help there, as well.