4 nights in Switzerland-Advice on itinerary please

I think you mean Gimmelwald. A Swiss Half Fare Card would pay for itself. It is 120CHF per person so if your total fares are 240CHF, it is a wash. Since you are including the Schilthorn, it should save you a few francs.

Spiez is a better place to stay than Interlaken before your train to Italy. We have not stayed overnight but have toured the charming town a couple of times while waiting for our train.

Most tourist stays in Switzerland are short, which is why they offer Swiss Travel Passes for 3 or 4 consecutive days, though not one for 5 days, which is the actual time you could possibly use one. Note that they're pre-validated for the dates you supply at purchase, so if you were going to buy a 4-day version in advance, you have to choose whether to have it working on the arrival day in Zurich or to work from day 2 to day 5 (to the border at Domodossola or Chiasso). They are also sold in stations there, including the airport station.

You'll spend a minimum of $250 per person for the routes mentioned, and probably more for the unnamed exploration routes. A Half-Fare Card is certainly a safe bet versus full-fare tickets.

Since you are asking for advice on your itinerary, I'll just state what I would do with the same time constraints.
I'll assume you get into Zurich mid-morning. If you're going to adjust/undo jetlag, why not do it in a better place than Zurich? Lucerne is MUCH more beautiful.

https://www.airpano.com/360Degree-VirtualTour.php?3D=Lucerne-Switzerland

(The 3 boats in that 360 degree panorama are docked out front of the train station.)

So, book a train to Lucerne (trip takes about an hour) and then eat lunch there. There's fast food in the station, or if you want to explore the town, there are lockers in the train station. If you are traveling light like Rick Steves advises, your luggage should fit.

Maybe a couple of hours in Lucerne. If it is good weather and you will make use of the trains and cable cars around Gimmelwald/Murren, then consider a Berner Oberland Pass, which will pay for all transportation from Lucerne on south to the Italian border. (Except for discounts on 2 highest mt. peaks, and you must take the somewhat slower train from Spiez on to Italy.)

Then take the train to Interlaken Ost (about 2 hours total, watch for the lovely Sarnersee about half way), get off at Interlaken Ost, find the Grindelwald/Lauterbrunnen train, usually on track 2A/B, and make sure your train car says "Lauterbrunnen" on the side.
Now you COULD go to Gimmelwald, and I see why Rick likes it because it is quaint and isolated (great for a travel writer), but Murren is much more centrally located, and your time is limited. Also there are 10X more places to stay in Murren. If you want to see the hikes out of Murren (pics and maps), click on my name and send me a private mail that you can later read by clicking on your name in the upper right of this page.

I would not waste another day and do more packing/unpacking by staying in Interlaken or Spiez. I did this exact route to Italy last summer (using the Berner Oberland Pass) and the trains out of Lauterbrunnen are reliable and every 30 min. and link up well with connections in Spiez. You can be in Milan, Italy in about 4 hours. I think we left Lauterbrunnen at 7:30 and were in Milan before noon. If staying in Murren just add another 30 min to get to Lauterbrunnen.
If you start looking at pics of Murren or Lauterbrunnen or Mannlichen, you'll see why staying in the alps is so much better than spending time in Zurich or Spiez. I've been in the Lauterbrunnen/Murren areas about a dozen times, and I try for 10 days at a time, so you can see why I'm trying to increase your nights there. Plus, there's always a chance of a rainy day or two, so each extra day can be huge.