Final update:
All solved - I am officially a dummy.
First, I installed the Sagawa module in unencapsulated form (slight mods to _Sagawa.php class and sagawa.php shipping module files), and this installed perfectly. After which I discovered I was missing a couple of custom functions needed only in the shipping modules.
After adding these in functions_addresses.php, I uninstalled the unencapsulated version and retried the now proven encapsulated version. Running uninstall correctly removed all configuration keys.
This is when I finally realized that installing the plugin does not create configuration keys - only the tarif table (which part I had already solved previously).
Installing the actual payment and shipping modules provided by the plugin then correctly inserted the configuration keys.

I hope this helps someone else when trouble-shooting in future.