The Lounge is a web based IRC client for the modern world, see https://thelounge.chat/
If you have a supporter account you can run a self-hosted private instance of The Lounge and connect to any IRC network.
SSH to the buildserver using: ssh buildserver
Install thelounge via npm: (https://thelounge.chat/docs/install-and-upgrade#from-npm-releases) npm install --unsafe-perm thelounge
Hop over to triton and add a user in thelounge: node node_modules/thelounge/index.js add <myusername>
Edit .thelounge/config.js and change the port to your supporter account assigned TCP port.
Start thelounge (in tmux/screen): node node_modules/thelounge/index.js start
Connect via web to http://supporter.blinkenshell.org:<yourport> and log in using the user you created previously
If you have a custom domain name and want to enable HTTPS via TLS certificate maybe it can be done using letsencrypt and DNS-01 challenge? There are options to specify cert files in .thelounge/config.js