Yes, his solution re-creates the partitions, and yes, you would then have to
reinstall (or maybe not, since the partition table would be identical), but
during the reinstall, you wouldn't have to make the partitions, you could
just install. The feeling I got from the web page was that this would
allow things to proceed normally.
As for why one kernel boots and the other doesn't, I don't know. I suspect
it's related to your bootloader and the fact that the installed kernel
comes from the same source as the partition table, but that's a total
guess.
Justin