Assuming you have your SSH server already configured (I'm using two Ubuntu machines so there's no setup required here), first connect to your second machine:
ssh -XC firstname.lastname@example.org
-X enables untrusted X11 forwarding (more secure than
-Y, ish), and
-C enables compression, which is important for making Firefox work well with this technique.
Now you can launch Firefox in that shell into the background:
firefox --no-remote &
--no-remote prevents Firefox from using your local machine's profiles, and
& sends the process into the background.
The last piece of the puzzle is to swap the following setting in
true and then restart Firefox:
gfx.xrender.enabled = true
All this together means that I seem to have a pretty performant copy of Firefox running through SSH even over my WiFi network, and I set up a keybinding in i3 to launch the browser as a one-off command, like this:
bindsym $mod+Ctrl+Shift+Return exec ssh -XCt email@example.com "firefox --no-remote"