1 - Create a container (Docker, Jails, maybe even chroot)
2 - Assign an ip to the container, NAT to it
3 - Install firefox on that container
4 - Run a SSHD server, enable X11 forwarding
5 - Mount the relevant container's folders to your root fs (eg: map $CONTAINER/.mozzila and $CONTAINER/Downloads to $HOME/jailed-browser/)
6 - Add an ssh config for quick alias
7 - Run `ssh container firefox` and profit
Here's a nice example using FreeBSD jails (I remember following this tutorial, everything worked out fine):
My experience with it, though, wasn't great. X11 forwarding through SSH was quite laggy (even after performing some optimizations on the connection). Good luck if you want to set-up audio/mic support. It's a nice solution for a one-time banking login, not for day-to-day use.
Thank you very much! I will give this a try immediately.