Remington's ORDNANCE Steel was always higher priced. When Remington introduce their John M. Browning designed Remington Autoloading Gun and their John D. Pedersen designed Remington Repeating Shotgun, they came with a Remington Steel barrel. For $6.75 extra, one could get your Autoloading Gun or Repeating Gun with an ORDNANCE Steel barrel --
On the Remington Hammerless Doubles the ORDNANCE Steel barrels were the same price as the Damascus barrels on the C-quality and above guns, but were $15 extra on the lower grades. List prices from the 1903-04 Remington Arms Co. catalogue --
Grade A ..............$45
Grade AE.............$50
Grade AR.............$45
Grade AER...........$50
Grade AO.............$60
Grade AEO...........$65
Extra barrels for AEO....$40 Extra barrels for AO...$37.50
Grade B...............$60
Grade BE.............$65
Grade BO.............$75
Grade BEO...........$80
Extra barrels for BEO....$47.50 Extra barrels for BO....$45.00
For all other grades extra barrels were half the price of the gun.
The Remington Steel barrels were only offered on the A-quality guns and after 1900 on the K-grades.
According to Semmer, some very late guns were produced with Krupp Steel barrels, but I've never seen one.