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Silly head
There are no size restraints on the head; both planks are way longer than is needed and we can go up to 5½" in the width.
I'm not suggesting this as a serious design, but it shows what might be done.

Semi-silly head
Before we leave the realms of silly, this design actually does give a straight pull on every string

Pretty plain
The slightly improved version of the sensible head. Is this too bland?
We'll leave it at that for now and probably come back later and do something entirely different.
Two thoughts occurred to me almost simultaneously: The machines are individual, so the head could be made with steps like an Emmons steel guitar. The machine posts have two holes, so they could be used like a normal Gibson or Fender type going through just one thickness of wood (around ½" to ⅝".) The wood will have plenty of depth if we use both mahogany and maple, so we can take the head down to a suitable depth and thickness, and maybe even angle it.

Here's a wooden version.
The router can do 'outside' sharp corners but not 'inside' ones.
The stepped walls would be not be added on but routed out of the solid mass of the wood of the head.

Second visualisation
What do you think of this?
Answers on a postcard please.
Some detail is lost here because it is scaled down from actual size. The photoshop document is 36" x 36". Actually that's not quite true; the original is upright and is 39" x 8". I changed the canvas size to 36" x 36", tilted it 50° and cropped it to fit.
Like the head?
Don't all shout at once.

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