I do not have time right now to digest all of this and to take action. However, I did manage to download and burn a Mini KDE iso of PCLinuxOS, which is also untested as yet, but which may serve as the LiveCD to follow Just18's suggestion.
By the way, that was why I had such a limited approach to the initial use of Gparted--I was running from a LiveCD of only Gparted and the minimal Debian that was on the Gparted disk. I had no access to the good Gparted interface available in PCLinuxOS, or the other support from a good, complete distro.
There is no rush, thankfully, for you to do this, so do make sure you read through the procedure a few times to get an overall view of it and will feel comfortable applying it.
Create mount points for the two partitions, and mount them at those mount points.
Copy the contents of the old to the new, and edit fstab to ensure the new is used as /home in place of the old.
I haven't tried this while using a Mini ISO, so it might be best to ensure that the commands I used above are all available to you before you start.
To do this check just use the command itself followed by the option for the help information .... like this
A response with the various options for the command used will let you know the command is available to you.
I expect that all used commands are immediately available and there would be no requirement to install through Synaptic ..... but I also expected the /mnt directory to exist in all ISO
So this is really only necessary to confirm the commands are all available before you start the procedure.
The Mini ISO should have no problems ...... and it is such a long time since I ran a Gparted LiveCD that I have no recollection of how it presents to the user.
Sorry about the crossed wires with that.
I have edited my detailed post to include the '-p' mkdir option to overcome an absence of the /mnt directory if that should be the case.
So please use the edited post for reference.
Let us know if there is anything else for which you need more detailed information.