Got a little more info out of Yamaha (like pulling teeth). Yamaha won't let customers talk to the tech people, you only get to talk to customer relations specialists and they don't know anything. Yamaha told me that tech support is handled by their dealers, and I told them the dealers don't know anything either. When I finished my last call with Yamaha, I called another big Yamaha dealer and asked about differences between the 2000iS and the 2000iSv2. Dealer's response: "What's a v2? Don't have one, never seen one, don't know when we'll have them in stock, don't know how they are different." All I could get out of Yamaha CS is that the v2 puts out cleaner sine wave power for computers and electronic devices, but the specs they sent me are identical for the two units.
Re the EF2400iS vs the EF2400iSHC, the "HC" stands for High Current. That version has a function similar to the larger generators that boosts output current to 20 amps (or maybe more, they don't know) for up to 10 seconds, specifically to start up A/C compressors and other high startup load motors. That could partially explain why some 2400s run A/C and some don't.