Darren and Mike -
Darren's washer is indeed a 1964 model Lady K, and Mike's is a 1963 Lady K. When the '64 model was introduced, it garnered a 900 series number, whereas the Ladies prior had been 800s (there was usually at least one other 800). This was done I believe because this left more series deliniation between the other 800s and the top dog, which by 1964 had the first 3-speed motors.
It is very possible that the first '64 models were made in summer or fall of 1963 or around that time, and that the '63 models continued in production WHILE the '64 models were made. There were seven running changes made to the '63 model as can be seen by the model number engineering revisions that come up on Sears' site, whereas there was only four revisions to the '64 unit.
The '63 model seems to have had a very prolific production run based on the sheer numbers of them that I've since seen. Same for the '65 model.
What I am getting as is that it IS very possible that Mike's machine was made in 1964. Dating a Kenmore can be confusing, but they have always done what looks like odd stuff. The '65 800 machine in fact was made into 1968 - I have one made in 1968 that is Avocado in color, which wasn't even around yet in 1965 and came with a plastic agitator instead of bakelight.
If you want to know for sure, look at your model numbers. Darren's should be something like 110.640490X (or 110.640590X if it's a suds model) and Mikes should be 110.630480X. Up through 1973, the first two characters to the right of the decimal indicate the model year of the machine, and the X in my example is where the engineering revision is found. Engineering revisions occurred when a part number changed in the original parts diagram. Timers, pumps, revisions to filters, belts, etc. all would get new numbers and thus cause revisions to ALL models they were being used in at that time.
G