OK I figured this out and wanted to report back in case anyone else has this issue down the road. Through more troubleshooting I traced the issue down to the configEncKeyAes.key file that's generated when you export your IIS config using the tool in the IIS Shared Configuration window.
I found that if I exported the config on the destination server and just used the key file generated and retained the configuration files from the source server the Shared Configuration would finally apply without freezing. All sites came over as expected. The only issue is any credentials saved in the config (e.g. custom AppPool credentials) could not be decrypted and had to be reset. This made sense since I was using a different key file than the one generated with the original export on the source server.
This led me to the site below that talked about the need to export the IIS WAS and Configuration Keys from the source server and import them on any other IIS nodes at play. Doing so immediately fixed the issue and the shared configuration applied without issue and the embedded credentials I had on a couple sites carried over as well.
troubleshooting-iis-shared-configuration
I've read several articles about deploying Shared Configuration and none of them mention this seemingly necessary step. But I'm finding that documentation and support around this feature leaves much to be desired.