I measured carefully, and found I could install a drawer. It is shallow and goes partway under the sink, but it is deep enough for a cutlery drawer, and in the perfect location for one. I used the tip-out "drawer" front on the drawer. It looks as if it came that way from the factory.
I bought the drawer with slides from "Shelves That Slide." Link is here
Ordering info is also below. You may need a different size.
The filler piece on the left side of the opening is just a piece of pine 1x2 that I cut to fit tightly. It's not glued or fastened in. The left-side slide keeps it in place.
One more thing- If anything in the left side of the drawer was piled higher than the drawer side it would drag on the underside of the sink. I figured clearances pretty closely.