HI, I have a extra t38 carbine cleaning rod. I do not see a a Nagoya stamp on it. I do have a t38 Nagoya carbine and the cleaning rod that came with that does not have one either. Are you sure they were marked?
Here is what I know thus far regarding the 4th series Nagoya 38 carbine production, all changes took place during that 100K run.
a) The butt plate went from flat to cupped in the 35K range
b) The metal finish went all blued in the 59K range
A mint example I got in the 37K range had a bright finish Chigusa proofed rod which had the outside part straw finished. Most bright rods I see have a dark to nearly black finish on the exterior part and that seems to be what happens to the original straw finish when handled by hands and exposed to the elements. You see this on lots of early Tokyo rifle parts that were strawed.
One example does not make my opinion correct, but if your carbine is an early 4th I would go for a bright Chigusa proofed rod. Note that the bright rods in 95% of the time have the coarse thread pattern 4 x 0.60 mm. you may see reconditioned rods that are blued every so often, but the majority of the blued examples that are Chigusa proofed have the fine thread pattern 4 x 0.50 mm which is identical to the threads on Type 99 rods.
Saw some carbine rods at the Dec. Phoenix show and they were in the $ 100 + range.