It looks like a good itinerary.
Arno will have to comment on costs, but, at first glance, i think you have reached the correct conclusion.
The nice thing about the Swiss Travel Pass is that you can change your mind or add a longer boat trip, or ride the bus, etc., and still just show the pass.
By the way, the spelling is "Schilthorn."
One concern about your plan.
You have allowed only one day in the Jungfrau region. It the weather up top is heavy clouds, you may be disappointed on Schilthorn (or Jungfraujoch). One way to learn more, besides local sources near Lauterbrunnen, is to talk to the tourist information office by track #1 in Luzern main station. You might go directly on Day 3, for example.
Re- the Rigi.
The lake is complicated. Get out a map.
That is a great trip. Note that from the valley station of the cableway descending from Rigi Kaltbad to Weggis you will have a 10-15 minute downhill walk to the boat dock. No shuttlebus. (In German, valley station is "Talstation." Means bottom station, more or less.)
Might want to have some sort of map available for that walk if your schedule is tight.. Check out the schedules carefully. The boat service back to Luzern is limited in Winter:
If you miss the boat, there is back up bus service running more frequently and later from Weggis Schifffstation to Küssnacht am Rigi train station, thence train to Luzern. Or, to Brunnen train station and thence to Luzern.
You will see some very nice northern parts of the lake on your way to/from Vitznau/Weggis.
I will say that, in my view, the best part is the part from Vitznau or Brunnen south to Flüelen. This link gives some ideas of that region among the other images:
This gives some ideas about the more northern parts: www.myswissalps.com/fo rum/topic/the-hammetschwand-lift.
Also, see attached images.
These images are not winter images. sorry. ;-(
Althopugh I do not think it is necessary, if your itineray has room and you are in the area, you probably would enjoy the "Urner See" -- the southern part of the lake.
The timetable will help you figure out your options. The boat landing at Flüelen, atthe southern tip of the lake is close to the tain staion.
There is a shoreline bus from Weggis to Brunnen Schiffsation, to also think about.
You have to decide how much to fit into a day. At least the boat rides don't tire you out. ;-)