I visited HB9 land last year (Interlaken/Thun area then time in Geneva), so a little way from Zurich, but found 2m to be fairly quiet up in the mountains. You may have better luck in Zurich, especially as you are quite close to the D and F borders, so aren’t reliant necessarily on local stations to chase you.
I monitored and called CQ every day at various times on the standard calling frequency of 145.500FM (standard for us in Europe anyway ) and managed 3 contacts in a two week holiday, two of which were French, just one HB station. As an American you may have better luck, as most Europeans probably choose to ignore Brit’s at the moment ha ha! I did find my calls in French and German helped elicit responses; certainly one French station spoke very little English, but my schoolboy French allowed me to converse for a good few minutes - at least, I think he understood me…
I also had some really useful help and HB9 advice from Paul @HB9DST so you may want to contact him for more up to date info.
If you hike high up in the mountains, take a look at REGA who provide an air ambulance/SAR service across HB9. https://www.rega.ch/en/operations/additional-services/emergency-radio.aspx
As Manuel says above, if you are patient and perhaps post a couple of alerts/spots where you can, you should be able to activate, if not qualify your planned summit. I found mobile phone coverage was pretty good, even up 2000m summits, so you should be able to post self spots to help the chasers find you. I imagine a weekend activation would be easier and may result in the odd S2S.
Good luck & let us all know how you get on.