John,
I realized that you could not just dump the resultant featurelayer 'outNALayer' to a table, however, you say you are successfully writing it to a .lyr file. (arcpy.SaveToLayerFile_management(outNALayer, workspace + "\\" + outLayerFile, "RELATIVE"))
a .lyr file can be used in the table to table tool directly. Would think that if the outLayerFile.lyr had the information to add it to ArcMap, that using it directly in the export would give the results that you are after.
Could be something to do with the nature of a layer file created for a na composite layer not letting you do it, I'm not sure.
Again, I don't have composite layers to examine/test, but curious what "changes" to the layer or outLayerFile.lyr file are made just by adding it to ArcMap? I was under the impression that arcpy can get the same information from the .lyr file that ArcMap can (however, the sub-layer could be and issue here).
I was only suggesting, that if ArcMap doesn't actually "change" any data/info when you add it to the map, thought you could skip that part. Would suspect that maybe this is the only way to 'extract' a sublayer from the .lyr, but just thought I'd throw this out there in case (since I can't test).
With my .lyr files (again, just basic datasets, not a composite layer), I get the same results if I table to table the .lyr file itself, vs, loading that into arcmap and dumping the table out.
R_
Further testing with a "group" layer, and I see that the TableToTable tool has issues and see's it as invalid input...... Thus the need to add to ArcMap..