Another update: if I make a partition with a proper name and size, then I can restore my partial backup there. Then I can successfully test and apply my BIS keys in HacDiskMount. It complains at startup, though (Attachment). I don't have backup of USER partition, so BIS3 key check fails there. Also, clearly my GPT is a mess.
Anyway, after some more thinking, I believe what I need is a rawnand.bin from another console, as my old eMMC is dead and I can not make my own one. rawnand.bin also contains GPT, which seems to be an essential part to make it all work properly. There is a gptrestorev1 payload, that can rebuild GPT, but it only works on 32Gb eMMC and I got a 64Gb version as a replacement =( No luck here. But restoring things from rawnand.bin to a bigger eMMC was never a problem in any of the eMMC upgrade manuals. It should work. Also raw NAND backup has USER partition in the right format. I think, I will be able to apply my BIS keys to it. Maybe I will also need BIS KEY 3 (crypt) and BIS KEY 3 (tweak) from the console, on which raw NAND backup was made to decrypt it and encrypt it with my own key, I'm not sure. Rather that this, I'm out of ideas for now.
Please, someone, share your rawnand.bin with me so I can proceed with trying to revive my lovely Switch... =(