Cool project. I've been collecting a list of automated tools for editing [1], which originated at Bell Labs with The Unix Writer's Workbench [2]. Rather than start from scratch, if you want to stick with JavaScript you might consider contributing to Titus Wormer's ReText [3]. Otherwise, we'd love for you to join us in building the Python-based Proselint [4].
Yes, it catches a few things that Grammarly doesn't catch (or have to pay premium to view) like missing the closing parenthesis, or forgetting a period at the end of the sentence (I'm using Grammarly on mobile; it's possible that I didn't see the error.) We have a ton of cases still to add, and since it's entirely focused on punctuation and small details, we hope it should catch more than standard grammar checkers.
1. https://github.com/amperser/proselint/blob/master/research/c...
2. https://www.princeton.edu/~hos/frs122/unixhist/text.htm
3. https://github.com/wooorm/retext/blob/master/doc/plugins.md
4. https://github.com/amperser/proselint