i3wm: two monitors, one browser per monitor (dual head kiosk)

You could assign specific class names to your Chromium instances and tie them to workspaces. So with 2 monitors config:

workspace 1 output HDMI1
workspace 2 output HDMI2

for_window [class="^chromium-no-1$"] move workspace number 1
for_window [class="^chromium-no-2$"] move workspace number 2

You'll need to start 2 browser instances with specific class values:

$ chromium-browser --class=chromium-no-1
$ chromium-browser --class=chromium-no-2