I glanced at the question while trying to figure out if I can answer, but didn't look too deeply into the question itself.
The final paragraph of the question is the one that would have been decisive for me:
How might the app reliably and securely persist information about each Main page instance, regardless of which browser instance, window or tab, so that the the server accurately recognizes the correct user/group session participant for that Main Page? Hidden field? localStorage? Something else? Pros and cons of different techniques?
It really feels like one that is asking us to design it all for you. You haven't addressed a problem that you are having. And while you may have some information about the backend design that is already firm, you haven't communicated this in the post.
There are two things that I've written here that seek to try to help people formulate a better question when trying to ask this:
The blue sky nature of the question - that we don't know what the problem that you are having with your design is. And thats where the comment that is on the question is addressing.
The pros and cons is one that we often see and is very difficult to answer. In part, because everyone regards the advantages and disadvantages of a given design (and the different designs is indeed far too wide open to be able to even have a chance at narrowing it down) will add their opinion. This often leads to rather short and unhelpful answers.
Hidden field pro: its simple
local storage con: you've got to use local storage and it's inconsistent across browsers
something else pro: Its something you haven't considered
yet something else con: Its something you haven't considered either
These are all "valid" answers to the question. And they aren't really helpful to you, or to the next person who comes along trying to ask a question about a similar design.
You've given us a requirement. Tell us about your design and specifically where you are having problems. If you are just asking for us to do a design, there are far too many ways for that to be done, and most will be incompatible with some part of your system.