You can make a github page for each project, but it walks me through a process that forces me to use their template and my own markdown, not able to actually upload html/css etc. I suppose I could create another github account though, but not sure if I want to do that every one-off site I want to put up.
You can definitely create github pages for each repo, using your own html/css/js. You just need to create a gh-pages branch [1]. If you just want to host a new static site, you can even create a new repo just for that, create a gh-pages branch, then make it the default branch and delete the master branch, leaving you with only the gh-pages content [2].
As far as I know you can create multiple sites on one account. I'm not sure what you mean about GitHub forcing you to use a template. For my homepage, I set up a new Git repo and used a Gulp module to deploy to it without any issues.