Ford itself likely did not apply the wood grain to the various dash and window molding components. For that matter, it is highly likely that many small stampings such as those under discussion were made by outside suppliers. Original dashes often have stamped numbers on their back sides that do not correspond to Ford's part numbering system, which supports this theory (see photo below of the back of a mint '32 dash; it's an early one so the '34' part of the stamping is obviously not date related). When Ford outsourced parts manufacture, they usually did so to at least two suppliers to ensure uninterrupted supply. Those suppliers might be located in the Dearborn area, but judging from the known location of some of Ford's outside suppliers of the period, that wasn't a necessary requirement.
For those of you with a copy of Lorin Sorensen's excellent book, "The Ford Shows", page 114 is devoted to a Motor Products Corporation (a Detroit company) working display booth in the Ford Exposition Building at the 1934 Century of Progress in Chicago wherein the workers actually applied graining to '34 instrument panels.
Different suppliers often had different techniques and capabilities, so while it is likely that there was more than one supplier of woodgraining, it wouldn't necessarily mean that the process used by them was identical in all respects as long as the suppliers' methods met Ford engineering's specifications. This could give rise to minor variations in the ink patterns on the finished work, for example.
Further, Ford did change the grain patterns during the course of model years. This happened extensively during the '32 model year and I have to spend some time at the BFRC in Dearborn to determine if there were ink pattern changes during the '33 and '34 model years. (Based on originals that I've seen, it appears that the base red color did not change during those two model years.)