Stumbled onto a Sublime Text plugin called Browser Refresh for Sublime Text.
Install it via Package Control, bind the refresh command and it’ll refresh the active window/tab in your browser(s)
ctrl+shift+r -> reloads last active firefox tab
No browser plugins. Just nice and simple.
At the time of writing this, the official github repo & package seems to be missing Linux functionality.
The issues list pointed me to this repo which seemed to work. Use at your own discretion.
I got Firefox reloading successfully from within Sublime Text 3 on Xubuntu 13.04
Chrome reloading didn’t work for me (would love more time to inspect why)