The fact that a change of Paper Type (both in the driver and on the printer), from Letterhead to Colored, changes the behaviour still suggests that the "Alternative Letterhead Mode" mechanism is involved.
You could check what the driver is instructing the printer to do by capturing the output of one of your problem print jobs (using the "Print to File" option in the Print dialogue), then analysing the resultant .prn file - this may (but may not) yield some clues.
Captured PCL5 and PCL6 print streams can be analysed using the PRN File Analyse tool in the PCL Paraphernalia application, available via http://www.pclparaphernalia.eu