Well, you could have also tied recovering your installation by using a Puppy Linux. I'd recommend using BookwormPup64. This can be written to a thumbdrive, and will run perfectly well from there.
To get the UUIDs just run blkid in terminal.
To copy one, just select it, then Rt Clk and hit Copy. To paste it somewhere else just RT Clk and paste.
if the wrong UUIDs are present at boot, that's going to show up in Grub, your bootloader. Probably in a file called grub.cfg, or menu.lst, or some other similar text file. Using blkid, you should be able to establish what the correct UUIDs are, and edit thm back in place.
Also aboard will be the program gparted. This will examine your disk and show you the partitions and contents graphically. You can check partitions with it or fix them -- not the same problem as a Grub UUID mixup, but possibly also a problem you faced.
As far as backing up goes, for the big linuxes, yes probably imaging the drive will be needed, since grub is often on a different partition that the rest of the linux installation, and you'll need both. For that the dd command in terminal is quite effective, but be absolutely sure you understand how to use it properly -- which drive is being imaged, and which is being written to, or it can wipe out the contents of your drive. I don't have a problem with it.
Puppy linux is easier to back up than the big linuxes because It is very compact (frugal installation) so you really only have to copy your save folder (or savefile if you use one). The save folder (or file) has all of the changes you made to the original puppy installation, and contains your user data. So if you back that up, you can easily restore customizations, installed programs and personal data, using the stock installation media. Grub problems are fixable by correction, no matter how bad, so really, backing up the savefolder, (or file) is all that is needed to be back in business.
Besides Puppy Linux, there is also EasyOS -- similar in many ways (same original author) but designed to use containers, if you like that kind of security isolation -- though it doesn't require their use -- it is particularly well suited to running off of a thumbdrive, though can also be installed frugally as a very compact OS.
I'm working presently on switching from Puppy Linux to EasyOS as my daily driver after over fifteen years with the former.