[guitarman2]

So what are my options for an SG with a chunky neck profile. It doesn't have to be "Nocaster" chunky but a much fuller profile than the more common slim taper. Classic 57's would be a plus.
Ideally wouldn't want to spend more than 1k.

 

[jdto]

You might check the 2016 Standard. They are chunkier and can be had for around $1k.

Some of the Special models also have fatter necks.

 

[Roryfan]

Early-mid 2000s Std. & Std. Faded had fat necks. The Fadeds had 490s which are quite close to 57s in both the neck & bridge position, whereas the glossy Stds. had a 498 in the bridge.

 

[vadsy]

You might check the 2016 Standard. They are chunkier and can be had for around $1k.

Some of the Special models also have fatter necks.

Agreed, you beat me to it but I was coming to say the same thing. The 2016 models had some chunkier necks to choose from, it was very noticeable.