Quick update:
Summary: The Plugin installer is a tricky little beast. The issues are related to my customizations.
Long version:
I decided to go ahead and start working on various changes to the plugins while thinking on how to debug, starting with the Sagawa module.
For the _Sagawa.php class I use ISO codes for prefectures rather than the names. After I made that change, I reran the installer, and while no configuration entries were made, I noticed that the tarifs table had been created.
While keeping the (not really installed except in name) module installed, I installed the Tarifs module and could access the table fine.
Thus, it is clear that my customizations are the issue here.
I haven't yet been able to get the module installer to run even though I believe I have made all necessary changes to the sagawa.php shipping modules file, but it does appear that the Plugin installer is doing a lot more than I expected - I thought I could install the module, then debug it afterwards as needed.
Unfortunately, it seems that it is a hard job to debug an encapsulated module, compared to a non-encapsulated one, as the Plugin installer does not seem to generate any logs. But it is what it is.