Brooklyn, sounds like you got a good gig, if you can make him happy.
Thin slices provide more surface area of the meat and therfore provides more flavor per sandwhich. Not to mention that the thinner slicer are inherently more tender. If the thin slices are falling apart, I would have to say that the brisket is slightly overcooked. I would suggest that you cut back on the cook time just a little and that should help firm up the slices. You obviously want a tender brisket, but even thin slices should hold together. This will make for some very yummy sliced brisket sammies.