I think a single coil in a les Paul style guitar is odd... if building a les Paul style body with a Floyd rose and HSH configuration seems like a far stretch then you could possibly custom order that body from pitbull guitars.

You should consider:

The tools you'll need, how much would it cost? (If you didn't have the recommended tools)
What wood to use, where to buy it from and how much? (good quality wood that is suitable for guitar building)
Is this the guitar you really want to build? Would it be a keeper? (Is this a guitar you wouldn't EVER lose interest in)
Is it really worth investing lots of $$$ on hardware and electronics for a guitar that might not satisfy your taste in the end?
Would getting the body and neck built for me be cheaper and easier than building it from scratch myself?
Does this guitar and its hardware suit my playing style?
Would I prefer spending the money I'm willing to spend on this guitar, on another guitar?
Do you place expenses over experience or vice versa?

That's all I could think of.