Shoot a video in iPhone 7 Plus' Portrait mode
No, you cannot do this without a jailbreak.(unless you were doing stop motion).

The workaround you mentioned would work, though. How to crop a video(cropping the frame around the subject): https://filmora.wondershare.com/video-editing-tips/free-video-croppers.html

You can record the screen like this using Quicktime:(I don't have an iPhone7 so I don't have portrait mode):