I would wait till the very end as well. Get your top 5 barrel flats all nice and smooth, and then drill it an install it. With some guns, like Lehighs and Bucks, the TH is located pretty high on the barrel flat (as is the lock). If you are bumping up against the smallest of extra steel margin on the flat for the TH liner, and then you file the upper quarter flat flat some more, you may expose the edge of the liner on on the upper quarter flat. It's probably not a safety issue, but it would certainly look like a building error.
If you're planning on engraving the top 3 flats, you may wish to even wait till you have smoothed down that engraving. I've yet to see a gun with engraving on the side flat(s), but I suppose some might be done, but certainly away from the lock area.