Copy mixer settings to another multitrack file

SteveG is correct that the only real way to do it is use your existing session as a template for a new one but you are way past that point so there is no 'conventional' way of doing it.

However, you could look at one of my Audition utilities sesx2sesx which should do the trick

The only way you can do this  is to save your wanted session properties as a template. You can't actually change a template in an existing session directly, although SuiteSpot might possibly have something to say about this in terms of what's in a session file - I'm not sure whether this is going to be possible or not,  but on the face of it, it's unlikely. Anyway, what you have to do is remove all of the files from your session and then use File>Export>Session as Template, and this will at least preserve your mixer settings and levels. If you export the session properties without removing the existing files, their presence in the session will also be saved - and that's almost certainly not a good idea if you are starting a new session; you just want the basic settings there.