That seems strange to me that the engine would make a difference. The part numbers that you listed are not the correct part numbers (I don’t believe). Here is the part numbers I use on my International Buses. Check them out. If you give me the last 8 digits of your vin number I can look it up and double check.
These assemblies are about $360 a piece: Left/Driver 3765681c93 Right/Passenger 3765682c93
If the only reason that you are changing them out is because they are cloudy than I would recommend going to AutoZone and buying the headlight restoration kit and giving that a try before buying new ones. If the only thing wrong with them are that they are cloudy.