If there are any paint stores in your area stop in and ask to see their mis-tints. Ask the manager to make you a deal. Not uncommon to be able to buy a quality paint for $5 a gallon or less when it has been made the wrong color. Use an exterior paint if possible. Stores in my area give unsold...
As a pro painter I'm just curious why you would dilute the latex and make a whitewash? I'm a big fan of DE but would dust the walls after the paint film had dried. I don't know if the DE would be of any benifit when it is applied to the whitewash in a wet state. What is on the walls currently...