Salzburg to Murren

Most train questions are answered by going to the railway company website.
For example, SBB (Swiss Federal Railways): https://www.sbb.ch/en
Enter a query Salzburg to Mürren or Gimmelwald (note spellings, or do you mean Grindelwald?) with a date and time and it will find you the quickest route.
via Munich and via Innsbruck (through the mountains) take similar time, nearly 9 hours. Note some of the Munich connections have a bus between Munich and Zürich, i.e. less comfort.

You can rent a car and drive it, but that has two problems:
1) A car rented in Austria must be returned in Austria, or you pay a large surcharge.
2) You cannot drive to Mürren or Gimmelwald. The road ends at Lauterbrunnen in the valley.

The trains go via Bern because that is the only way, the mountains are in the way! Same by road quickest route via Bern.
The alternative, by rail or road, is via Luzern and the Brünig Pass, that is more scenic but slower.

I essentially did what you describe, albeit in segments. I took an OBB train to SG Buchs. (I did that because I had a swiss rail pass and I just wanted to get to the border) From there I went to Zurich and then Luzern. (We spent three days in Luzern) The Golden Pass Train route goes from Luzern to Interlocken (and actually beyond to Lake Geneva, FYI). I was going to Lauterbrunnen so I switched trains at Interlocken Ost. Murren is literally on the mountain just above Lauterbrunnen. We took a Gondola to Murren/Gimmelwald, but I believe there is a train station as well. My guess is that there would be a Murren bound train at Interlocken.
The Swiss Rail people are VERY helpful and efficient. They would print an itinerary and explain which gates to go to and transfer times. We used the Swiss trains quite a bit and I think there was one time that the train was more than a minute or two late, and then it was only ten minutes or so.
Of the places we went to in Switzerland, Luzern and Gimmelwald were favorites.
Incidentally, one of the days we stayed in Salzburg, we took a day trip to Munich. The Bayern ticket makes it crazy cheap. There were three of us and the ticket was about 50 Euro round trip for the three of us. You have to make sure to use the correct machine and train. The train ride was about 1 1/4 hrs. When we went to Luzern from Salzburg I know we did not go thru Munich. I'm not sure what the exact route was but I know we went thru Linz and Innsbruck.
I have rented a car in Europe(France). I would not rent in Switzerland, their public transportation is wonderful and so far there has not been a place in Switzerland that we couldn't get to by train/bus. Also, even if you do not purchase a Swiss Pass, city buses are free with a hotel reservation. A Swiss Pass also lets you use the gondola from Lauterbrunnen to Gimmelwald and Murren.
Lastly, Switzerland is very small. So when it seems like certain train routes are "out of the way", keep in mind that these cities are actually very close to each other. I believe Zurich and Luzern were an hour apart. Bern was about an hour from Luzern and Basil is about two hours from luzern.
Have Fun!

How much slower is it to go through the mountains vs. Munich

I think you'll find "going through the mountains" is the fastest, most direct way. Take the Railjet to Zurich and go from there.

Grindelwald is a village across the valley from Lauterbrunnen. Gimmelwald is right by Murren (a gondola ride or walk, and adorably cute).