LVM and rescuing systems

Your description sounds roughly right. I don't do a lot of disk upgrades on my home PCs, and the improving financial prospects at work have meant we can afford an actual sysadmin - so it's possible we're missing a step.

From dim memory I recall "do something with GRUB" is the trickiest bit, but the last time I did this (and thus the sharpest in my mind) it was with RAID 1 plus I was simultaneously trying to switch a Fedora system from ordinary LVM to LUKS encrypted LVM by hand, which in hindsight was not a good idea although I'm using that system to post this so it clearly worked.