Hah! they're not so "secure" now that you posted them here
A couple questions/thoughts:
Are you going to carve the top and back like a 335 or make it flat?
No reason not to use single coils if you like them. Single coils are often used with chambered guitars, like the Tele thinline.
Here's a thought: to me, 335s are very bulky. Since you're doing the single coil thing, you could downsize the body and streamline it some, like a CS336 or an Ibanez AM series guitar. I'm a little biased (this is my site)
In the drawing, it looks like there is no neck angle, and as a result, the fretboard sits very high above the body (The 335 copies I've had all have an angled back neck). In fact, it looks like you might have bridge height problems if you build it as shown - the string height measures 0.88" at the bridge, while the tunomatics on my guitars are 5/8 to 3/4.
If you built the neck piece with an angle and dropped it down at the joint, it would look better, setup better, and you'd have better alignment and contour at the heel.
I would look carefully at the geometry, and massage it so that it works to your advantage.
-Sven