@dmoglin, thanks for the additional info - very helpful.
So if Alternate Host is your best bet, this bullet from the Zoom Support article for Alternate Host will govern the Alternate Host's means to start the meeting:
- The alternative host can start the meeting using the join link in the email or calendar invite sent to them by the host. The meeting will not display in the upcoming meetings list in the desktop client, mobile app, or web page for alternative hosts.
Us volunteers in the Zoom Community don’t have a way to handle feature requests, so if having these meetings show up on the Alternate Hosts list is a change you'd like to see, please use this Zoom web page to make a feature request directly to Zoom staff:
https://www.zoom.us/feed
Currently, only sessions scheduled by you or authorized Scheduling Privilege holders will be shown on the web site or your Zoom client. If you have Scheduling Privileges, your session displays will have a drop-down selector to show all or only a certain user's sessions...
On zoom.us:

On Zoom Windows PC client:

Meetings you are attending, registered for, or alternate host for are not included in your list.
Alternate hosts can join the meeting before the host arrives, and will have host permission. But if they don't have the meeting saved in their calendar (or yellow sticky notes, or something!), then they probably won't get there. 😐