I think I've completed the puzzle, but I have one small doubt gnawing away at me...
In my completed grid, with all substitutions made, there is a single Down answer that does not appear in Chambers, but it does appear in the OED. Should this cause any concern? The preamble only references Chambers, but it does also offer the somewhat vaguer requirement that "the final grid contains all real words and phrases," with "real" possibly suggesting a bit more latitude.