Typically I like doing 1 1/2" or less thickness, just need a slightly smaller headstock.
Doing a 1" or 1 1/4" body, would require you to make the pickups and hardware a little more "external" to the body (pickup routes and cavity routes are shallow)........ as far as neckdive is concerned, if it's headless, no problems there, unless it's a heavier body wood (for a headstock). As far as pots, you'd need to use a "bourns".....:
