I have much love for this story :) It's so cool that you used the holo-room, which was pretty much forgotten about about it served its plot!device role - and you used it so well! I love the idea of John setting up an obstacle course.
It's so cool that it's not some big story of how they got together, but just an accident. I love the description in this, and the slow, quiet way John and Elizabeth come to grips with having bumped into each other and then don't let go. The description of John's look is great, especially with the other times Elizabeth's seen it (my favourite is the serenade in the cafeteria, but the giggling goodnight made me grin).
The hologram interrupting them is laugh-out-loud funny (and "the Ancient version of the talking paperclip" cracked me up; I loathed that paperclip!). I also like how Elizabeth decides that 'talk' and 'slow down' don't need to be said and moves on to going somewhere more private. Perfect!
You may have guessed from the above, but I loved this story! Please procrastinate in this fashion more often :) Thanks for writing!