That looks like a very good itinerary.
Thanks for the dates. I really like this following hike, and you will too, if you have decent weather, and if the trail is open that early in June.
Two years ago I was up there on June 15th,. The trail had just opened within a day or so of that date. Lots of snow still around. It had blocked the trail until just a day or so before. Unfortunately, we had only a slight break in the clouds, so chose not to make the hike.
The later in June that you can get to the Jungfrau region, the better.
Unfortunately, this is too far in advance to ofer a prediction on weather or trail conditions. Once you are in the region, check with tourist offices or the staff at train stations.
You asked about recommendation for section 3. Here is more detail on the option that I recommended earlier in the thread. Personally, if I were doing it, and, mind you, everyone has personal preferences, I'd go from Lugano to Flüelen in your section 3, then continue to Luzern by boat or by train. I'd probably take the lake boat from Flüelen to Luzern independently, or as part of the Gotthard Panoramic Express:
That does take more time than staying with the train as I note in the following paragraph.
Or, you could simply stay on the train and go Luzern (you might have to change at Arth Goldau...some of the trains from Italy go to Zürich, some to Luzern, and they arrange a really easy change of trains at Arth Goldau if you happen to be on the wrong one. Get off, walk across the platform, and get on).
Then, I'd move Wengen two days later. At that time of year, even a couple of days makes a difference for hiking in the Jungfrau region.
Since you plan to overnight in Zürich, you can go to Zürich from Wengen on the day before you fly out.
Just my personal take on the options.