You were right: in one continuous shot the laptop stays put, so a single screen fits the whole way, no per-scene tracking needed. The scrolling TrueBuild site now sits inside the glass and tracks the angle start to finish, with the "new job enquiry", "5-star review" and "job booked in" pings popping through the day.
The light drifts toward evening and the pings do the rest. Grab the pieces below if you ever want to re-cut it.
The stills every clip was generated from. 01-master-golden-morning is the one the final timelapse came off. The kf- frames are the per-scene keyframes (morning / dog / afternoon / golden / family / night) if you want to regen individual beats.