Head to head coverage might work but wastes lots of water. The reason I want you to scale your yard on paper is so you can draw a bunch of triangles and some circles on a separate piece of paper. I am going to have you move those triangles and circles over your plot find the best possible place to place your sprinkler heads.
You are going to build the equilateral triangles based on the sprinkler manufacturer performance data. You will build your triangles on the published maximum reach of the sprinklers minus 10-20 percent because all performance sheets for anything lie.
I need to ask. We know you have possible erectile sprinkler head dysfunction. Any other envy issues in designing this system we all need to know about? If a system could be built that used your flow rate and water pressure perfectly but did not wake the neighborhood to say, "I have a lawn and I am going to water it with golf course rainjets? You would be alright?"
You will build the triangles based on the performance of the sprinklers you choose. You may need a couple watering circuits and may only be able to water only half your lawn, perfectly, at a time. Each point of the triangle is a sprinkler head location.
You said it was a weird shape so slide your triangle grid around. You can buy sprinkler heads, templates or adjust the water wasting rainjets with little clips. Be creative.
I am sure box stores do not carry them but I used to specify Toro low drift, finger jet type lawn sprinklers all the time. You mentioned wind drift. May I talk you into an irrigation timer to water when it is healthiest for turf anyhow? And winds are usually not so strong?
Oh well. Here is the drawing showing triangles and complete coverage. You will grasp the concept. You cannot get it trying head to head, I promise.