I also completed this repair successfully without removing the screen. I kept the screen at a 90 degree angle using the iPhone’s box and a rubber band as pictured in Step 13. I was nervous about bumping it while doing the rest of the steps and stretching the display cables too much, but it worked.
When re-attaching the Lightning connector cable, be extra sure that it’s really well-connected. This connector doesn’t make a very firm attachment, and it can even be partially connected. I finished this repair, put everything back together, and the home button was not working. I was convinced I had damaged the home button flex cable, and it looked like my wife was going to be consigned to using the AssistiveTouch virtual home button for the rest of the phone’s life. In the end, it turned out that THIS cable was not firmly attached… yet other functions such as battery charging were still working.
Did a better job connecting it, and the home button with TouchID came back to life. Since the positioning of the cable governs how it connects to its port, and the cable sticks to the surface below it with adhesive, you may need to gently pull the cable back up, and make sure it’s pressed back down in just the right spot to get a firm connection to the cable port.