Hi CLor,
I don't think you're missing something - Square's Online Website editor is a bit different animal - meaning from my experience, it's not setup the way many ISPs or Web Hosting services are designed. Square wants to make it easy for the non-coder and/or Developer which is understandable.
As for how I like to work, my site hosting service provides a clean slate whereas I can code anything the way I want it. I basically create my website on my local computer and can test scripts, code, etc., until I'm satisfied, from there I can FTP (upload) my entire site and/or any particular page changes/updates to my Host Server.
As for Square Online, I have not figured out how to the same thing so my work around is to use my site to show my work using my scripts / code and then link my site to my Square Online Site for purchases. At least this makes everything easy for me and as my Square Online Site blends in with my original site - the transaction between the two is seamless from the customer's perspective. And I don't have to be concerned with transferring my Domain Name to Square. Bottom line, for me there's no additional cost as I can use Square's basic Online site for free, I get a shopping cart and only have to pay fees when I have a sale. It's a sweet partnership.
This is way more than the scope of this community so you may want visit the Square Developer Forum - as there are folks more familiar with what can be done. Hopefully, you will find a solution there. If anyone else has some thoughts - please share.
