Well, I wish you were using more than two whole plots, but I understand that you have a practical constraint.
Here is a custom design definition that I think captures the essential characteristics as you explained them.
This design is the result.
The warning in red is by the custom design. Here is a script that will re-produce the custom design platform for you to study and possible use. You can copy it here and paste it into a new script window.
DOE(
Custom Design,
{Add Response( Maximize, "Chlorophyll", ., ., . ),
Add Factor( Categorical, {"Water Limited", "Well Watered"}, "Drought", 1 ),
Add Factor( Categorical, {"x", "y", "z"}, "Genotype", 0 ),
Set Random Seed( 809122516 ), Number of Starts( 13501 ), Add Term( {1, 0} ),
Add Term( {1, 1} ), Add Term( {2, 1} ), Add Term( {1, 1}, {2, 1} ),
Set N Whole Plots( 2 ), Set Sample Size( 24 ), Simulate Responses( 0 ),
Save X Matrix( 0 )}
);