The easiest way to get your site up and hosted inside SharePoint would be to rename all your .html files to .aspx and upload the entire thing into a document library including folders with your js and css files.
Your users would need to be logged in to see the pages and you would only need to modify your existing solution to change any .html links in the content to .aspx (I would just write a quick batch file to do this).
You can keep the exact format and structure you currently have so you don't need your supporting css and js to be in the Style Library, they can just be in the same document library in their own folders so your existing relative links will keep working.