Our purpose on this forum is to aid travelers to Switzerland. We don't want to leave a mistaken impression for them. And, since you are publishing in your local paper, as a journalist, you would likely wish for fact checking. Ithink your style of writing is well suited to an average reader who has not traveled to Switzerland, and will be read by many in your town. Even more reason for accuracy.
<<"Part 4-Sadly, we left Wengen and the Lauterbrunnen Valley and arrived in Lucerne. ............ On our first day in Lucerne, we headed to Grindelwald First.">>
As I noted before, unless you took a 2 and 1/2 hour train ride back to Grindelwald after you got to Luzern, which seems unlikely, you misplaced Grindelwald-First. It is as you so clearly describe it in a very compelling fashion, but it is near the Jungfrau. It is above the town of Grindelwald in the valley of the Black Lütschine, over the Männlichen ridge from the Lauterbrunnen Valley.
Cost of the First excursion -
This site gives ticket prices:
www.jungfrau.ch/filead min/Prospekte_und_Bros chueren/Grindelwald-First_Prospekt.pdf
With the two STP's for the Adults, and your 14 year old daughter, each of the three of you would have paid 30 CHF round trip from Grindelwald to Grindelwald -First and return, and the adults 46 CHF each for the First Flyer and your daughter 40 CHF. Total, 222 CHF.
Indeed, if you add lunches at (guess) 30 CHF, you get to 312 CHF.
<<"Most mountaintop excursions could cost you $500 for 3 people and that is including a discount for having a Swiss travel pass from the railways">>
I wondered how you could spend 500 USD or CHF on that trip up to First and come out with a total "out of pocket" of $850 for your entire journey.
<<"An eleven day trip to Switzerland for 3 people for $850 out of pocket is a pretty good deal in my opinion.">> That section of your report is confusing to me. And, I'd say that it is certainly a good deal.
When I said "50" I was mistakenly thinking about only one person, and only the trip up and down. That was my error. I did not include the Flyer or such activities in my estimate, because they may not be present on all mountain excursions. For instance, the trip with STP from Vitznau or Arth-Goldau to Rigi-Kulm is free. Also, Schilthorn and Stanserhorn are free. Pilatus is discounted 50% to 36CHF per person, round trip..
On each of those mountains you can eat, but there are (if I recall correctly) no costly activities up there. (No sure if there is fee for any sort of James Bond stuff on Schilthorn.) There are some on the way up and down to Kriens.
I feel strongly that saying "Most mountaintop excursions could cost you $500 for 3...." leaves an impression that is not appropriate or accurate. Perhaps it is because the word "excursion" does not bring to mind for me the activities available on some but far from all mountain tops. We may be using the word differently.
<<"We began our one hour hike up the mountain to where the base of the lift begins. It was an exhausting hike, but the views along the way made it worth the hike! We boarded the tunnel elevator and zoomed up to the top of the lift.">>
Since the part of the Felsenweg between Bürgenstock ( actually, the Restaurant 1879 on the road to Honegg) and the elevator (and then the elevator ride) is by far the easiest and, arguably, the most scenic way to get up to Hammetschwand, it is important to have the correct timing. I have done that walk (in both directions about 8 or 10 times).
You gave this link to Switzerland Mobility:
www.schweizmobil.ch/en /hiking-in-switzerland/routes/rou te-0566.html
I'll add a topo map.
map.geo.admin.ch/?topic=swisstopo&lang=e n&bgLayer=ch.swisstopo .pixelkarte-farbe&catalogNodes=139 2,1538,1396,1430,1436& layers=ch.swisstopo.sw isstlm3d-wanderwege&E=2672586.7 3&N=1205443.11&zoom=7
The figure that you quote, and that is stated in the link to Switzerland mobility is the time for a complete round trip from Bürgenstock to the foot of the elevator, onward to Känzeli ( which is a more difficult mountain trail), then to Honegg, and a return along a trail parallel to and just above the road from Honegg to Bürgenstock. It does not include the elevator ride.
The altitude profile given in the Switzerland mobility link shows a hike a bit over 5 km long. In fact, if I were to undertake that walk, it would almost certainly take me ( as a slowpoke,with no Swiss genes ) well over the stated time.
The walk to the foot of the elevator is about 1 to 1 1/4 km. Roughly, 2/3 to 3/4 of a mile. 20 or 30 minutes is correct for that section if you take it easy. 15 if you are fit and walk quickly.
I have attached a photograph taken from the Rigi, with marks to show the location of the beginning of the trail near the resort ( an old picture; the resort has expanded) , the foot of the elevator, and the top of the elevat0r. The trail continues along the side of the cliff to the left of the foot of the elevator.
I added a few (which are also in the link I provided earlier) to show more about Hammetschwand. I liked your image 576, which is a very nice telephoto shot looking down from the elevator platform at Hammetschwand.
If you took an hour, you took some other route, in my opinion. If you come up the back side from Trogen, and do not use the elevator, it would be a steep climb. And, the trail signs on top show 1 hr 10 minutes back to Bürgenstock, and 35-45 minutes to Honegg, going down the back side.
One of the nicest things about walking or hiking - in fact travel in general - in Switzerland is the superb maps and the long list of special trails presented on on Switzerland mobility.
www.schweizmobil.ch/en /wanderland/wanderland .html
And, the wealth of data on almost any subject in a variety of media on the internet is a rich resource.
Used thoughtfully, they can give really accurate guidance.