Biel-Bienne to Interlaken - 6:30 - 8:30 AM
When looking at the train schedules, take a look at what other options you have around the time you want to leave. I don’t see a 6:30 departure time, perhaps you were looking at 6:24 via Belp? If you leave at 6:22 it only takes 1h 37min, not two hours.
Interlaken to Jungfraujoch - 9:00 - 10:40 AM - via eiger express
Do you want half an hour in Interlaken?
Use sbb.ch or the SBB app for routes and times. Enter Biel (which is always written Biel/Bienne because Biel is bilingual German/French, but I just use the German - this is perfectly fine) with your destination being Jungfraujoch.
Biel - Jungfraujoch
7:22 departure gets you at Jungfraujoch at 10:41. Choose an earlier departure only if you want to have extra time somewhere along the way.
As far as your reservation to descend Jungfraujoch, you can get on any train going down that has room, so if you are ready to go earlier you can see if there is free space on the train and head down to Wengen.
I personally do not think you need to plan each subsequent step to the minute, it is enough to know what train you want to take back to Biel and keep an eye on things so that you can catch that train. The absolute latest you can leave Mürren is 21:51, but your plan is to leave before then and that is a good choice, it gives you a little in reserve just in case.
I also would skip Lauterbrunnen and go directly to Mürren. I would not walk to Gimmelwald and definitely not make a dinner reservation. You already have a very full day and to add on an exact location and time that you need to be at for dinner makes no sense to me. You can grab something at any of a number of places in Mürren or get a grocery store supper/take away/and even eat on the train if needed.
Keeping things planned where you need to - train to Jungfraujoch - is important, but keeping the rest of the day very loose so that you can adapt to the weather, your mood/energy level, what looks interesting at the time, etc. seems like a much more enjoyable way to spend the day, at least this is what I usually do with day trips and it has, for me, been the best way to see a lot while still having a non-stressful time.
