Nice diagrams. The dark and light colors clearly show where your bare spots are.

The literature I've seen recommend that sprinkler heads should be laid out "head to head". That means one sprinkler head should reach out and spray another sprinkler head. Figure 1 is an example of this. Figure 4 is close.
The center circle needs to be enlarged to reach the top and bottom edges, and the half circles on the top and bottom need to expand to touch each other in the middle.

A great resource for irrigations systems is http://www.irrigationtutorials.com/

Like Saxophone mentioned, you need true head to head coverage. Head to head coverage means that the outside radious of one sprinkler head reaches the next sprinkler head. Just because the spray patterns overlap, does not mean that it is true head to head coverage.

Although there are a couple of pictures that are close, the only diagram that shows true head to head coverage is # 5.

Hope this helps.

Curtis

Here is a link that might be useful: EvergreenSprinklers.com