Went back to the original BaCH thread to find this, that I posted in 2011.
The first 20 BaCH NRs were all white (but I can't remember if they had belly cuts). I believe they were thick bodied.
The first series has a belly cut. And the body is the thickest of all BaCHbirds: 43mm. It has a veneer on both sides. The veneer on the top side covers up potentiometer holes that weren't drilled in the right position.
The second set of 30 were all thin bodied with a belly cut. There were 10 white, 10 black and 10 Sonic Blue in that series. These had nice, thin necks.
Correct
The third series (up to current) were all thick bodied with no belly cut and were available in single and dual pups.
The body of the series III isn't really that thick.
Here's a series III BTH-1
The Honeybursts were all single pup but the Trans Cherry were available in both single and dual pups. A little later dual pup Honeybursts were available. These had slightly thicker necks.
Here's an early Honeyburst BTH-1
The later Honeybursts have a volute at the back of the headstock.
In the series V there were also Black ones and Sonic blue and Transparent Cherry (or Burgundy) with armcut.
Here's a series V BTH-2 with armcut and belly cut
And a series V BTH-1 with armcut and belly cut