An update to this information:

JavaScript's "Temporal" API has an algorithm for doing arithmetic on
timestamps with timezones[1].

I still think I'm going with removing the requirement to be able to add
timestamps with timezones, as it is quite complex. Even for non-timezone
situations, the "PlainDate"[2] addition method disambiguates “according
to the cultural conventions of that calendar's users.” It’s quite
complicated.

[1]:
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Temporal/ZonedDateTime/add
[2]:
https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Temporal/PlainDate/add

-- Peter McGoron