You need to move the stripe portion to the view cart page in order to skip the checkout page. You can't leave the stripe portion on the checkout page if you don't want it to exist at all.
Save a backup of all of the pages before you get started. The custom scripts and updates to the payments.js file and checkout and confirm pages will be obsolete once you don't use those pages.
It is unfortunate that I wasted time working on the checkout page in premium support but that is what I was tasked to do, and when I was done it was exactly what you had asked for, integrating it into the checkout and confirm pages. It is only now you are wanting to eliminate those pages entirely. We call this a scope change or a change of requirements (some people call it shooting at a moving target).
I'll help you through the forum as much as I can so you can get it fixed. The first step will be to move the square code onto the cart page. Just remove the checkout button that is there and put the checkout with square form below the cart.