How can I fix a date that changes by 4 years and 1 day when pasted between Excel workbooks

Problem

In Excel dates are represented internally by a floating point number where the integer part is the number of days since "some date" and the fractional part is how far into that day (hence the time). You can see this if you change the format of a date - like 4/10/2009 to a number 39905. But when pas…