"A pH of 5,7, or 9? Hm how long do you think it would take to distill?"
Just to clarify, that quote was saying at those pH's (5,7 or 9) DEET was stable, and hydrolysis did NOT take place. I was using it as an example of why you would have to go well beyond pH 10 for hydrolysis to occur at a reasonable rate. But after reading the paper I posted above, I would be going with H2SO4 instead of NaOH.
This table was taken from the paper I referenced in a post above;
Transition state activity coefficients in the acid-catalyzed hydrolysis of amides
Looking at that table, at the analogous compound N,N-Diethylbenzamide, whereas DEET would have the systematic nomenclature = N,N-Diethyl-3-methylbenzamide, an extra methyl group at locant 3 on the ring. For N,N-Diethylbenzamide the greatest rate contstant is achieved @ 70.9*C in about 25% Sulfuric acid.