Late '60s and '70s SGs tend be be fairly slim-necked and narrow at the nut, as far as I know, so they probably won't meet your chucky neck requirements.
If the chunky neck really is important, it narrows the options quite a lot, at least with current models. All SG Customs, the '61 reissue, nearly all Custom Shop models seem to have the '60s slim taper neck, unfortunately.
Alex makes a good point about the neck joint. Much as I love SGs, I've started to be wary of them for that very reason. The weakest seems to be the early '60s neck joint with a little "step" at the sides of the neck. The current neck joint is a bit bulkier at the heel but does seem to be a lot stronger.