I am probably not understand your use-case correctly but there's a `--new-window` flag on the firefox binary. You can use that to open new windows under the same profile.
It will refuse to start.
Do the following: sudo -EHs su, then as root sudo -EH -u {username} firefox --new-window
I'll leave to you the exercise of learning what the flags do, and implicitly why it fails in your case.