>> Day 4: Zurich to Geneva, Geneva to Montreux, Montreux to Lucerne (via Golden Pass), Lucerne to Zurich
If it were me, I would plan to put the best scenery at the beginning of the day, when you are still fresh enough to enjoy it to the full: i.e. travel first to Luzern, then the Golden Pass route to Montreux. That will take just over 6 hours.
After spending a bit of time in Montreux along the lakeside, I would skip Geneva and take the fastest route back to Zürich (usually via Lausanne).
Sunset will be about 8pm. Make sure you get to Lausanne before then, so you can appreciate the beauty of the Lavaux vineyard terraces (a UNESCO World Heritage site) before dark.
You might also want to avoid the commuter rush out of Lausanne, although without luggage that shouldn't be too much of a concern. If I remember rightly, most of them will have alighted by the time you get to Yverdon-les-Bains.
The fast route back to Zürich (skipping Geneva) will take between 2.75-3.0 hours.
>> Day 5: Zurich to Lucerne, Lucerne to Weggis by boat, Weggis to Rigi by cable car, Rigi to Virznau, Vitznau to Lucerne by boat, back to Zurich
The cable car from Weggis to Rigi Kaltbad is closed for maintenance from 3–27 Apr 2018. You can go up from Vitznau and down via Arth-Goldau if you like.
If you will be doing this trip on 1 April or 2 April, you could consider doing it in reverse. When I went up to the Rigi from Vitznau, the train was full on departure from Vitznau. Those joining the train at Rigi Kaltbad (from the cable car) had to stand (although it's only about 12 minutes).
>> Day 6: Zurich to Bern, Bern to Interlaken, Interlaken to Lucerne, back to Zurich.
This would be a repeat of some of Day 4. I would skip Interlaken and travel from Zürich to Luzern (via Arth-Goldau for some nice lake scenery along the Zugersee), then to Bern via the Emmental (put via Trubschachen into your timetable search). That would take around 3 hours. I would then spend the day in Bern, before returning to Zürich by the fastest route.