An update before I leave town for two weeks... I have a convention and a training to attend for work. See you on the other side!
After doing much research, we found that these anchors are what we need. There are a few different brands; all require a special $250 driver that is attached to a hammer drill and cost around $5 each. They are inserted into the mortar joints through pre-drilled pilot holes (also drilled with a hammer drill). We need 350 of them.
Our mason decided he didn't feel comfortable doing the work, so we asked a mason who specializes in this sort of work to come and give a quote.
The damage? $2676.
This includes the $1500 or so in materials. It's JUST for inserting the ties; we will have the first mason do the patching of the holes when he finishes up the brick work.
It's also a lot of money.
My father-in-law is a stone cutter/worker by trade, and has offered to come and help us do it ourselves. We can save almost $1000, even after we buy the special driver... which we might be able to sell off after we are done.
Of course, this won't happen for another two weeks.... lots to think on!