Having serious problems trying to set up train reservations

https://www.sbb.ch/en
You might not even need to book everything--care to share the itinerary?

Sure! Multithanks for the help
Sept 14 fly Boston to Zurich
Sept 15 Zurich airport to Appenzell
Sept 17 Appenzell to Lucerne
Sept 19 Lucerne to Lugano
Sept 21 Lugano to Pontresina
Sept 23 Pontresina to Zermatt
Sept 25 Zermatt to Lausanne
Sept 27 Lauzanne to Murren
Sept 30 Murren to Bern
OCt 1 Bern to Zurich
OCt 3 fly Zurich to Boston

This should help you: https://www.myswissalps.com/swisstravelpass/howtouse

Do you really want to move every two days?

We are discussing that. What would you leave out?

What are your interests?
You are kind of all over the place, but I would try to stay in one place at least four nights at some point.

Do you actually require reservations?

We usually just walkup and purchase tickets. Sometimes we're close to the train station the day before, and I'll just walk in to pickup tickets. Except during holidays, I've never been turned away.

But there again I'm traveling in other countries--other than Switzerland.

The only reservations you need are if you are taking special tourist excursions.

Sept 19 Lucerne to Lugano, only if you plan on taking the Gotthard Panorama Express.
https://www.sbb.ch/en/leisure-holidays/trains-trips/rail-travel-specialtrains/panorama-trips/gotthard-panorama-express/purchasing.html

Sept 21 Lugano to Pontresina, only if you plan on taking the once daily bus from Lugano to Tirano and the Bernina Express to Pontresina.
https://shop.rhb.ch/en/bernina-express

Sept 23 Pontresina to Zermatt, only if you plan in taking the Glacier Express
https://shop.glacierexpress.ch/gex_en/specials/daytrips/glacier-express

Other than that, no other reservations are needed or even available. All Swiss trains are open seating.

That's part of my question. If I don't have to, I won't. These sales declines are wasting a huge amount of time.

The easiest thing for you is to just buy the STP once you are here. You can just get it from the Railway station at the airport. No need to complicate things.
Then for most trains you do not need reservations, as has already been pointed out. This is mass transit. Just find your train and get on. Show your pass when requested. Do not overthink this.

Thank you for your reply. We have the STPs. I am concerned about needing reservations in advance, but from what I am reading, I really only have to worry about the 4 scenic trips, which is extremely helpful.

Credit cards are apparently not the issue

I believe SBB uses 2-factor ID required for on-line credit card purchases, so if you do not have that set up on your cards, and you probably don't, the transaction never reaches your credit card. If you have American Express, I have hear that works as it is not considered a bank card, but a travel card.

Or use your cellphone as before, if that worked, keep it up.

Hello Sam, It worked when I bought the STPs, but not when I tried to buy the reservations. If I only need reservations for scenic routes, that is a significant help.

Our interests are old cities, museums and seeing & being in the mountains, riding trams & gondolas.

Train travel in Switzerland is mass transit. Switzerland has an nationwide integrated mass transit system, and the railways are just the top level in the hierarchy. Like the subway is in many cities. Its just turn up and go, used by ordinary people for their every day business. People who would be rather upset if they had to reserve trains in order to do something mundane as getting groceries...

Hello, Thank you all so much for your thoughts. I live in a very remote area and don't have anyone to bounce ideas off of. Based on your thoughts, I'm not worrying about reservations unless I do the special scenic trains and I have updated our itinerary:
Sept 14 fly Boston to Zurich
Sept 15 Zurich airport to Appenzell
Sept 17 Appenzell to Lucerne
Sept 20 Lucerne to Zermatt
Sept 24 Zermatt to Lausanne
Sept 27 Lauzanne to Murren
Sept 30 Murren to Bern
Oct 1 Bern to Zurich
Oct 3 fly Zurich to Boston
I'm still debating adding a day at Lauzanne or Bern instead of Zermatt. Thank you again for taking the time to comment.

I'd suggest using the one of the nights in Bern for more nights in Murren. While Bern is great, the Alps are far more spectacular , and it gives you an extra day for hopefully good weather. In fact, I'd take another day from Zermatt and add it to Murren. No one is ever ready to leave that area.
The Swiss regional trains run on the exact same tracks as the panoramic trains. On the regional trains you do not need seat reservations. These trains are much less crowded, and the windows open, making for great picture taking. We rode this route on the regional trains for the Bernina Express route, and were quite happy. The regional trains are very clean and quite comfortable, and offer more flexibleschedule options, which is great in the event of a bad weather day.
Have a wonderful trip in this beautiful country!

Well, the OP is only spending one night in Bern.

I like this order of travel better, as it is less total time on trains and fewer pack-up-and-move-on-and-unpack days

Sept 14 fly Boston to Zurich
Sept 15 Zurich airport to Zermatt (3 1/2 hours to Zermatt)
Sept 18 Zermatt to Lausanne
Sept 21 Lausanne to Murren, visit Bern as a day trip from Murren.
Sept 26 Murren to Luzern
Sept 29 Luzern to Appenzell
Oct 1 Appenzell to Zurich
Oct 3 fly Zurich to Boston

What kind of Swiss Travel Pass did you get?

Sam, thank you for the suggestions. I do see your logic. We each got consecutive 15-day 2nd class passes

I've found that reservations are not usually required in Switzerland, except (as previously mentioned) for the premium tourist trains like the Bernina Express. Last time I flew into ZRH, I went to one of the on-site ticket offices and bought tickets for my onward trip. It was very easy. As I recall, there are two sections to the ticket office..... one for local Swiss trains and one for long distance (out-of-country) trains. I'm not sure if that's still the same?

I often buy tickets the day before travel at a local ticket office, and that method has always worked well. These days I also have the option of buying tickets on my smartphone with the SBB app.

You do not even need reservations for the Bernina Express if you stay in the first two or three cars. Only the panoramic cars require reservations and surcharge. And often the normal cars are less crowded too...