Update:
The kits arrived, and I managed to get my iPod open with only minor damage to the back cover. Well, maybe medium damage. I replaced the battery and removed the hard drive, but had a little trouble getting the SSD connected. One of the ribbon controllers had to be switched, and then when you put it in, it goes upside-down from the way you think it should. The connector is backwards, and tricky to get to stay in, so I concluded that it couldn't possibly go that way, as any sane person would. Nope, it goes that way.
So I got the system to recognize the new drive, got iTunes to reload from scratch, and it came up. It only recognizes 128Gb, which is better than 0Gb. Someone on the boards at the Zif site said that the 256Gb won't work at all in a 6G Classic, which mine is. The kit is supposed to be for the 7G, but I found a site that said the only difference is that the 7G is thinner because the HD is single platter, not double. But they're wrong; the motherboard is different because the 7G will recognize 256Gb and the 6G won't.
But it works, and if 128Gb is all I can put into it anyway, then I'll keep the kits and just go with 'em. The 128Gb kits were the same price as the 256Gb.