The personalised section breaks the 4th wall and talks directly to the viewer by name (also mentions their job title).
All the sections are prerecorded since she knows the recipient's info.
It is important that the sequence of videos runs as smoothly as possible... a gap of a fraction of a second might be acceptable, but anything more (waiting for the 2nd or 3rd video to buffer) would spoil the effect.
My host is DreamHost
and I notice that they have a licensed version of JWPlayer
available to all their customers. I see that this accepts playlists as input, so might be able to use this as a solution - but only if the transitions between videos are essentially seamless as described above.