At least your heads will have the right part number.
Mine are the 12559853 (1997-00) heads and while they are the same casting the part number is a dead givaway that this is an older motor.
There might be a milling and restamping job for me in the future.
I thought the year you started building your car was a factor too. I heard you had 3 years grace from the start of your build. Otherwise you're engine would have to be about the last thing to buy before rego.
I would definitely put forward that the 2001 LS1 motor is the same as the 2003 motor going by the casting numbers etc and that the ECU itself hasn't changed either, just the maps. Tell them you have had the 2003 map burnt into your ECU when you had the VATS disabled.
Cheers