Other than Arctic Fox (older code base), all the other browsers are exactly the same except for their user interface. So new moon, interweb, and spider web are all based on UXP and are equally the same. If the older 28.4.1 new moon still works, that means upstream broke something (or purposely removed something) in their newer 28.8.x releases. Not much we can do about that but wait, and hope they fix it.
In that case, I hope you will not yet drop New Moon from your collection...? It is still needed.
As for gmail, again, they should all work (except maybe AF), as they are all the same code base. However, why not use a dedicated email client? WebMail is so bloated. I'd suggest spidermail, sylpheed, gnumail etc. Otherwise you can add a user agent override in about:config of any of those browsers and "fake" a newer browser, which usually fixes the "outdated browser" warnings
In fact, I AM using an email client (YAM), and that is the reason I get those serious security alerts !-) As I have to be regularly several weeks away from my machine without being able to connect from the client, Gmail forgets the location/hardware and thinks that there is an intruder who has broken my account, and locks the access untill I login via an up-to-date browser and clear the alert! This happens also with the browser connection itself, but there I can bypass it by answering the security question. With email client, that is not possible.
So, are there ready-made user agents from which to choose, or do you have to somehow define them yourself? What information do you have to input? I suppose this is the trick which in some browsers is called 'spoofing'?