I have not been following this discussion. Sorry if I missed something (on
vacation). I am not sure what you mean by kernels are toast. I know the
expression, but doubt your problem lies with the kernel. Perhaps it is a
grub problem or something else. Grub points to the kernel and headers. If
the kernel does not load then it is grub's fault. Re-installing can destroy
data, so be careful. Also advice can vary with the version of Ubuntu. The
latest installer will pick up the installation and attempt to upgrade it.
Previous versions did not.

What I would do:

If you are worried about losing data, then first boot the Live CD and backup
data to another device.

If grub is NOT working: Use the Live CD to repair grub.
https://help.ubuntu.com/community/Grub2#Reinstalling%20GRUB2

If grub is working. Then I would boot into text mode and look at the boot
process and see what it is having a problem with.

Finally, if all else fails you can re-install. If you do NOT format then it
will attempt to repair the old installation. You need to choose the manual
installation option and have your wits about you. Back up just in case.