Gimmelwald to Salzburg - Train

I see if you leave at 9:30 you will get to Salzburg by 18:03. There are about 5 changes involved.
The Swiss and German rails don't have reserved seats. What could of course mess up your schedule is if one train is late where there are tight connections. You have to look at your layovers to see if there would be opportunity to eat something. Or bring your own stuff from a grocery store.
this site has schedules:
https://www.bahn.com/en/view/index.shtml

When we left Mürren early to get the multiple trains to Paris, the hotel put a cold breakfast out for us -- bread, cheese, fruit which we bagged up and ate along the way. I believe there's a Co-op grocery in/near Interlaken station.

The train changes are all early on in the trip, getting out of the Jungfrau area and you would have to make them wherever you go. And it is the same changes you made getting to Gimmelwald.
Once you get to Zürich, it is one train from Zürich to Salzburg. This train runs every 2 hours.

Trains in Switzerland do not have reservations, tickets are valid on any train. But the train from Zürich to Salzburg does have reserved seats, and does give a discount for advance purchase. This is an Austrian train, run by Austrian Railways (ÖBB).
You need to buy these tickets in advance, which will include the reserved seats. Then get the train/cable car from Gimmelwald which will connect to it at Zürich (and have tickets for that trip!)
I don't see how not having reservations causes a problem. Nobody on the Swiss trains will have a reservation, you just get on.

Gimmelwald (Schilthornbahn) dep 09:30, Cableway, Stechelberg (Schilthornbahn) arr 09:35
Stechelberg, Schilthornbahn dep 09:42, Bus 141, Lauterbrunnen, Bahnhof arr 09:55
Lauterbrunnen dep 10:02, Interlaken Ost arr 10:23
Interlaken Ost dep 10:30, IC 61, Bern arr 11:24
Bern dep 11:32, IC 1, Zürich HB arr 12:28
Zürich HB dep 12:40, RJ 167 Railjet, Salzburg Hbf arr 18:03

I would buy as much food and drink as you need in a supermarket on the day before, then you are prepared.

The trip between Zurich and Salzburg has some very scenic sectors between Schagens and Innsbruck. Be sure to book a train that goes through that route (like the Railjet mentioned above) and not one that goes via München Hbf

or the earliest combination is 7:30 cable car to Salzburg by 16:21, changing Stechelberg, Lauterbrunnen, Interlaken Ost, Bern, and Zürich:-

07:30
Stechelberg (Schilthornbahn)
07:35

BUS 141 41014
Richtung Lauterbrunnen, Bahnhof
Erwartete Auslastung
07:42
Lauterbrunnen, Bahnhof
07:55

Lauterbrunnen, Gleis 2
R 128
Richtung Interlaken Ost
08:02
Interlaken Ost, Gleis 2A
08:23

Station/Stop Time Platform Products Further information
Interlaken Ost dep 08:30 5 IC 1062 Intercity Direction: Basel SBB
Bern arr 09:24 4
Transfer time 8 min.

Bern dep 09:32 7 IC 711 Intercity Direction: St. Gallen(CH)
Zürich HB arr 10:28 33
Transfer time 12 min.

Zürich HB dep 10:40 8 RJ 165 railjet Direction: Budapest-Keleti
Bicycles conveyed - subject to reservation , Reservation optional , Bordrestaurant , Partially, snacks and beverages available (Buchs SG --> Salzburg Hbf), handy/quiet zones , Children's cinema (Buchs SG --> Salzburg Hbf), Speise- und Getränkeservice am Platz in der 1. Klasse (Zürich HB --> Buchs SG), Wifi available
Salzburg Hbf arr 16:21 4

Thank you all so much for your help! Super helpful!

Also, there's a Nordsee (fish) restaurant at Zurich station -- we shared a delicious fish meal there waiting for the Salzburg train. (I prefer a longer connection to one that I have to worry about.)