Some actual sources
Okay, so I'd like to edit a few things, but first I'd like to post here to avoid edit wars
1. Dragon II and III are real, also known as Dragon PIP and PIP II respectively. No primary source supports the existence of Super Dragon, which I believe is the result of confusion with Dragon III.
2. I do not believe Dragon II+ exists. Dragon II has the same motor as base Dragon, extending the guidance wire just results in the missile falling out of the sky at a roughly a kilomter. B2113 is the only source for such a range, and I'm still dubious of it.
3. Okay, I managed to track down the 1990 manual for the Dragon, couldn't figure out where the Mk 1 came from. Seems to match with this 1986 appropriations hearing (page 662) where the new warhead is said to be about 1lb heavier, though by 1988 it's "under two pounds" heavier
4. Per the 1988 hearing linked above, the Dragon III has 1500 meter range.
5. Per this 1987 hearing, Dragon PIP/Dragon II is an 85% improvement in penetration. 85% of 330mm is 280mm, so ~610mm/24 inches.
6. Per this 1988 hearing, Dragon III is the 1,500 meter range version and weighs 52lb. As the new day/night tracker weighs 16lb per here, this suggests that Dragon III is 36lb without tracker. It also has a dual shaped charge head, and is now laser homing The ~6lb increase over Dragon II would be the new motor, new seeker, and extra charge in front of the retained Dragon II warhead.
7. Per the 1986 hearing (page 498), Dragon III's dual-charge warhead is "several hundred millimeters" more powerful than SMAW's anti-armor round, which is stated at 600mm (okay, technically it says that SMAW is several hundred millimeters less powerful than improved Dragon, but whatever). This would put the Dragon III at 800-900mm penetration.
A such: Dragon III is a thing, Super isn't. Base Dragon is 330mm/13", Dragon II is 610mm/24", Dragon III is 800mm/31.5" to 900mm/35.4" penetration. Base and II are 1,000m range, III is 1,500m. Dragon II+ is probably not a real thing.