I created two measures...(i gave them color names, but you could do as you did as well).

then put the OtherYearsColors on the color mark

In the attached I changed your COLOR calc to look only at 2013.  Then there is an ELSE section that says PREVIOUS_VALUE

That calc is a table calc that says to grab the value from the previous cell.

When that goes onto the sheet, tableau defaults to looking at TABLE(across), which in your case is exactly what you want.  2014 looks at 2013.  2015 looks at 2014, which had grabbed its value from 2013.  Etc.

... and Nicole beat me to it.

Powerful table_calc function, PREVIOUS_VALUE!

Store it in your bag of tricks. 

...although yours was more elegant, Joe!

"Elegance" is all behinds the scenes.  Whether you plant the string beans in this-corner of the garden, or that-corner, in the end you get to harvest string beans. 

The key was planting string beans (or PREVIOUS_VALUE).

This also could have been done with LODs, and thereby no table calc (or PREVIOUS_VALUE) would be necessary.  But in this case I found PREVIOUS_VALUE to be easier.  Someone else might come along and say that LODs would be easier.

Cool thing, Tableau.  Lots of ways to get from here-to-there.