Re: Where to have custom guitars made??
"No matter the shape" and "V, Explorer, and SG" are two different things. If you want to hand-draw a guitar shape and have someone build it for you, you are probably looking at a built-by-hand-one-at-a-time one-person shop.
Warmoth does have V, Explorer and SG shapes, though those will be bolt-ons.
Perhaps because of the nature of set-neck builds, it seems to be a lot easier to find bolt-on/Fender-style custom builders than Gibson-style ones. For the latter, try Dunable Guitars, though their stock models have unconventional shapes.