I noticed your ID sticker is labeled a1977 and it's a 1978 model. My sticker is labeled 1978 and everything on my bike indicates it must be a 1979 as all the parts are like a 1980. Is this common?
As TexasKZ said, production would typically start later in the year before the "model year". There was a thread where we discussed the specific timing for the 1978 Z1R (D1) but I can't find it now. Basically, between a member who worked at Kawasaki in Nebraska, and another who worked for a dealer, we figured out that the emissions and safety regulations in California changed on January 1st, 1978, and the Z1R-D1 did not meet the new standards. That means that every single "1978" Z1R-D1 imported into the US was manufactured before 1/1/1978. My own research suggests that about 9000 D1 Z1Rs were imported into the US, with the rest of the D1 Z1Rs sent to other markets, for a total production of about 17k units.
If your bike has a frame number on the head tube, and it starts with KZT00D, then you should be able to figure out if it's a D1, D2, or D3. If your serial number is between KZT00D-000101 and KZT00D-017392, then it's a "1978" Z1R-D1. If it's within that range, but above 9000 or 10,000 or so, it is a bike that was not originally sold in US.
If it is in fact a D2, it's incredibly rare. The serial numbers suggest that there were very few of these bikes made, and I think they all went to Australia. But the frame numbers are somewhat documented.
One source gives D1 frame # as ending at KZT00D-017392, and D3 starting at KZT00D-017801. Presumably the D2 is between these.
www.zedder.com/Info/78%20KZ1000-D1%20Z1-R.htm
www.zedder.com/Info/80%20KZ1000-D3%20Z1-R.htm
The model recognition book gives a starting frame number of KZT00D-017501 for the D2. So that would be a maximum of 300 D2 bikes made, but it could be less, and I don't think anyone really knows.
One more detail.
Tony Sculpher's Z1R
book mentioned that he belies the D2 bikes were likely assembled in April 1979, and were probably assembled over a period of 2-3 days. You mention that your sticker has a date of 1978, so chances are that it's not a D2.
Where are you located? Want to post a picture of the head tube sticker?