We worked on filling in the vault today for a few hours and made some good progress. I started on my own but found it extremely difficult to manage each of the tasks involved. There are basically three tasks involved here: one mason to place the tile, one chemist to mix mortar almost constantly, and one person to work ahead of the mason to size tiles and cut them as needed. Alone, I worked at a snail's pace but once help arrived we were able to work efficiently and complete a good portion of the infill.
It became clear to us how important it is for the former arches (those on the outside edge) to be built accurately because any imperfection in the arch affects the surface of the vault. If the arch flattens out - and one of ours does - the surface does the same. We've been trying to "correct" this to some extent as we complete the infill.
I found that laying out the tiles for the infill is actually much easier than for the arches since tiles are placed with mortar on at least two sides. The two mortar joints mean there is more surface area bonded. As I worked on the infill it felt like I could let go of the tile much faster compared to when working on the arches where there was only one mortar joint.
Also, big thanks to Josh Berliner (PennDesign, M.Arch '15) for helping out today and taking photos!