There is a simpler way. Use Firefox for the game. Create multiple profiles - one for each account you use, in each profile login into a different account and put the indicator to "remember me". Choose in firefox settings to restore the windows from last session. Then open all the servers you want for the same account on the same browser/profile in different tabs.
If you close this browser/profile and then open it again and it opens up and immediately loads the last server you were on in the last tab that was active. If you do not switch tabs it does not load others. Once you do switch to another tab, it loads another server. It's really convenient.
To save on the setup time make a model profile where all the addons and scripts are installed, and then make multiple copies of the profile, all the copies will have the addons and the scripts ready and you only have to login once into each account.