We found that the DropDownList was being initialized before the Window. The solution was to use k-ng-delay on the DropDownList and reference the window it was embedded in.
We found our solution in the documentation on "nesting widgets". The example given there is for a tab strip, but we aren't having the issue on tab strips, only when we use widgets inside Kendo Windows.
In answer to Dimo's question, we did not have any enforced z-index styles in our CSS that effected our DropDownList.