Smooth App Demo Video Compositing

I already have the core footage in which a phone is being used, along with MP4 screen-captures and a few static images from the app. Your task is to composite those assets onto the device so the interface looks like it was filmed in-camera—no visible edges, jitters, or mismatched colors... (Budget: $30 - $250 USD, Jobs: After Effects, Color Grading, Motion Graphics, Video Editing, Video Post-editing, Video Processing, Video Production, Video Services)