Hey, very cool project.
This is really a javascript framework question, so if you got the code working in your browser normally, you can take that code, then serve it with HtmlService, and it'll run in AppsScripts platform. I suggest looking at using flexbox specification.
For a complicated project like this, it'll be worth investigating the different javascript frameworks that are available. I prefer using svelte.js, but I don't have a lot of tutorials to share right now. Just this repo:
Basically I can write the web browser stuff locally on my computer quickly, and not have the slower appscripts refreshing when I develop.
Vue.js also seems to be pretty good fit as well.
Adam