Mark, many thanks once again for your help with this! The steps all made sense and really helped me to "stay on track", and I have now managed to successfully transfer my site to the new XAMPP stack.
At step 2, I got an error ("The phpMyAdmin configuration storage is not completely configured, some extended features have been deactivated. Find out why. Or alternately go to 'Operations' tab of any database to set it up there.") This was displayed after clicking on "Admin" next to mySQL in the XAMPP control panel for the new installation. Clicking on "Find out why" displays a page with configuration info, and the following settings are listed as "not OK":
$cfg['Servers'][$i]['favorite'] ... not OK
Persistent favorite tables: Disabled
$cfg['Servers'][$i]['central_columns'] ... not OK
Managing Central list of columns: Disabled
I'm not sure what this meant and whether it mattered, so I ignored the error message and continued by importing the joomla.sql file generated in step 1.
Next I hit a size warning:
Warning: POST Content-Length of 37065247 bytes exceeds the limit of 8388608 bytes in Unknown on line 0
My joomla.sql file is 35MB. I then went into php.ini and changed some values: upped upload_max_filesize to 50M, and post_max_size=0 (i.e. disabling the limit), and tried again and this time it worked.
Finally, I copied the site (from the old htdocs to the new htdocs) and - tadaah! - my site is there, running on the new XAMPP stack.
Now I'm off to attempt the Joomla upgrade itself. Fingers crossed.