I got the problem fixed with the Amiga OS 3.9 / 3.1.4 upgrade fixed. The installer is doing something to the SYS:classes/gadgets or SYS:classes/images files. I initially assumed it was the "chooser.gadget" or the "bevel.image" file that was overwritten, as those are the only two files that the installer overwrites. Copying them from a known working folder individually did not seem to solve it, but when I copied the ENTIRE contents of the SYS:classes/images and SYS:classes/gadgets folders from a working installation to the corrupted one, it works!
Note that this was tested on three different installs - two of which were Amiga OS 3.9 with Amiga OS 3.1.4 installed over it using the script, and the third was just a native AmigaOS 3.9 install.
Until the devs fix the issue with the installer, the best solution is to back up your entire "SYS:Classes" folder prior to installation, and manually restore it when you are done... If not things like Amidock, the entire prefs files, and anything that needs resource.library will totally fail.
I will reach out to Matthew Leahman directly in case he does not catch this thread.